Dakshina Moorthy Sthothram Sloka 6

सदाशिव समारम्भाम् शंकराचार्य मध्यमाम्
अस्मद् आचार्य पर्यन्ताम् वंदे गुरु परम्पराम्

In the fifth sloka, Shankacharya outlined how we mistake ourselves to be either the deham(body) , or prana( life force) or as chalam budhi ( fleeting mind) or even as shunya( void). Based on who we think we are, different philosophies originate. For e.g as in Charvaka philosophy it is taken as Deham only , as does modern materialistic science. In Buddhism there are various trends. Shankacharya tries to refute the most prominent among the challengers of vedanta namely Madhyamika Buddhism.

In Madhyamika Buddhism or the middle way , the self is understood as the void. In fact not only the self , but everything is treated as void. The adisthanam of everything is considered to be emptiness. They make various arguments for this. One of the arguments favoring emptiness is that all things are a dependent arising. So many conditions are required for that object to exist that you can hardly call the existence as svabhavam. An existence is nothing but the totality of conditions imposed on that object. Essentially the object cannot exist on its own. When one of the conditions changes the object also changes or disappears. Note that this doesn't mean that the object doesn't exist. Essentially what this means that an object is just a bundle of causes and not an object. It resolves into nothing when the causes go. So its essential nature is nothing. When philosophers discuss some object what they are interested is not how the object appears, but on what it really is. This is why sometimes they seem a little dry and arcane.

Now deep sleep state is taken as an example by them as supporting the void. In deep sleep nothing is experienced. So our essential consciousness also should be emptiness, since it resolves into emptiness when the external dependent conditions such as sensory perception and thinking disappears. Some categories claim that there is nothing like the atma at all. All things including consciousness is just emptiness appearing as a dependent arising. It is this claim that the self is emptiness that Sankacharya tries to refute in this Sloka 6.

In order to understand this , we need to see how we experience the world in Jagrat and Svapnam. Consider this simple case. Suppose you are looking at some object. Now behind the seeing process, there seems to be a Seer, the process of seeing and the seen object collectively called the Triputi. Most importantly there is a Seer-I. What happens when we close the eyes. The Seer-I is not experienced and the triputhi vanishes. But hearing might go on. So the Hearer-I remains.
So waking state actually is a mixture of Seer-I , Hearer-I, Thinker-I and so on. In Dream state there is only the Thinker-I. When we close one organ, the I doesn't actually vanish. It is just withdrawn or that aspect of the I becomes unmanifest. But I continues. So the waking state is nothing but a mixture of various Qualified I experiences . Here Qualified I means Seer-I , Hearer-I and so on.
This is the Vikshepa shakti  of Maya . The qualified Is provide us a vision of the outside universe through its projecting power.

What happens during deep sleep?. What happens is that the Qualified Is are withdrawn, but the I remains. Then you might ask which I? There is no sense organs and there is no mind also. So what I is present?. What sankacharya says is this. The I that remains is the unqualified I .This unqualified I is not available for any vyavahara since no instruments or pramanams are there. Or the unqualified I is non -transactional I. This is much like space. You cannot do much with space. It is not available for doing anything unlike say an object. With objects you can do something. But with space you can hardly do anything. So deep sleep is like this. Consciousness remains as unqualified. But here you can see that much like space , it is a presence. Just because there are no objects doesnt mean that space doesnt exist.  Only thing is it is not available for vyavaharam. This is called the avarana shakti of maya. So here the vikshepa shakti is lost , but avarana shakti is predominant.

When the avarana shakti is predominant, only the general I is present . No qualified Is are retained. This is much like eclipsing of the sun or moon. When an eclipse goes on , the Sun is not extinguished. It is just covered with the shadow of the moon. Because it appears dark doesn't mean it is not shining underneath. It is just covered. राहुग्रस्तदिवाकरेन्दुसदृशो is what he says. Just as the sun and moon are eclipsed by the Chaya graha , the I is also covered, but the I remains shining underneath as general San-Maatrah satah. Here in the case of self, the shadow is maya or illusion. मायासमाच्छादनात्.

Now a doubt arises. If consciousness is not available for transaction , how do we say that it is still there in deep sleep. In jagrat and svapna it is understandable. However in deep sleep it is not evident. This is precisely the crux. Experiences in the world are all just perceived by the mind. Since the mind is absent , mind says it is not possible to say . So it is the mind that says I was not there. However sankacharya says the waker प्रबोधसमये realizes that I slept well. The term recognition is important. Recognition means i understand it is the same I who started sleeping who has now waken up. Recognition is the key word here. I donot feel that I was non existent. In anubhava of consciousness i feel that I was asleep. There is a continuity of me that i recognize. This is illustrated by the term प्रत्यभिज्ञायते.
So shankracharya uses the anubhava pramana to refute the claim by shunya vadha that i am non existent or emptiness. The continuity is always there. 

With this let us see the sixth sloka 

राहुग्रस्तदिवाकरेन्दुसदृशो मायासमाच्छादनात्
सन्मात्रः करणोपसंहरणतो योऽभूत्सुषुप्तः पुमान् ।
प्रागस्वाप्समिति प्रबोधसमये यः प्रत्यभिज्ञायते
तस्मै श्रीगुरुमूर्तये नम इदं श्रीदक्षिणामूर्तये ॥६॥Raahu-Grasta-Divaakare[a-I]ndu-Sadrsho Maayaa-Sama-[A]acchaadanaat
San-Maatrah Karanno[a-U]pasangharannato Yo(a-A]bhuut-Sussuptah Pumaan |
Praag-Asvaapsam-Iti Prabodha-Samaye Yah Pratyabhijnyaayate
Tasmai Shrii-Guru-Muurtaye Nama Idam Shrii-Dakssinnaamuurtaye ||6||


( Just as the sun and moon are eclipsed by the Rahu or shadow planet, Maya uses it avarana shakiti to cover the self during deep sleep. However the I remains its unqualified existence which is the reason why the waking person recognizes that he himself was the sleeper . I prostrate that supreme principle which makes me understand the pure and eternal I.)