kAshI vR^ikAndhaka sharAsana bANa ga~NgA 
	sambhUti nAmakR^iti samvadanAdi udantai: |
svokti ambarIShabhaya shApamukhaishcha shambhum 
	tvannighnamIkshi tavatAm iha kashsharaNya: ||

Meaning:

iha Ikshi tavatAm 		- For those in this world who understand,
udantai: 			- through the history of
kAShI 				- Kasi,
vR^ika 				- Vrukasura,
andhaka 			- Andhakasura,
sharAsana 			- the bow,
bANa 				- Banasura,
ga~Nga 				- Ganga,
sambhUti 			- his own birth,
nAmakR^iti 			- getting a name,
samvadana 			- dialog with others,
Adi 				- etc;
sva ukti 			- by his own words;
ambarISha bhaya 		- through the fear of Ambarisha; and
shApa mukhai: cha 		- by being cursed, etc;
shambhum 			- that Shiva
tvad nighnam 			- is subject to You,
ka: 				- who else is there
sharaNya: 			- to surrender to?

Vyakhyana Saram:
There are many ways to determine the supremacy of Sriman Narayana. One of them is the events in itihasas and puranas. Therefore, Swami Desikan takes a few events in this shloka and establishes His supremacy.

The phrase 'udantai:' should be taken with each of Kashi, Vruka, Andhaka, etc. These events are taken by Thirumazhisai Azhvar in his prabandhams - "kAysinaththa kAsi mannan vakran pavuNdiran", "muNdan nIRan makkaL veppu mOdiyangi Odidak kaNdu nANi vANanukku iranginAn em mAyanE", etc.

Through these events, Vedanta Desikan shows that Shiva is subject to the Lord and shows that He is the only one to whom one can surrender as said in "kaNNan allAl illai kaNdIr saraN".

The events described in this shloka are:

Kashi - An asura called Paundarika carried a conch and a discus and went around claiming that he was Vasudeva. Sri Krishna killed him with His Sudarshana discus. Sudarshana also cut the head of the king of Kashi who had come in support of Paundarika. The son of the king of Kashi became upset and performed penance to Shiva. Through Shiva he obtained a demon and tried to burn Dwaraka with it. Sudarshana defeated the demon who turned back on the prince of Kashi and killed him. Sudarshana then burned the city of Kashi. Thus the boon of Shiva to the prince of Kashi failed.

Vrukasura - This asura was also known as Bhasmasura. He prayed for a long time to Shiva and obtained the boon that if he placed his hand on anyone's head that person would be destroyed. To test the boon, he then attempted to place his hand on Shiva's head. Shiva surrendered to the Lord. Sriman Narayana then asked the asura to test the boon by placing his hand on his own head. The asura did so and was destroyed.

Andhakasura - This asura went into battle with Shiva. Shiva killed him with his weapon. From the blood of the asura, many more asuras came forth and attacked Shiva who then surrendered to Sriman Narayana. The Lord then created a creature that drank the asura's blood and Shiva was thereby saved.

Bow - This is the event of the Shiva and Vishnu bows in Sri Ramayanam. It is also the event of Shiva burning Tripura with his bow through the aid of Sriman Narayana.

Banasura - Banasura's daughter Ushai fell in love with Sri Krishna's grandson Aniruddha. Through her friend Chitralekha's help, she carried away Aniruddha and kept him with her. Hearing about this, Banasura became angry and attacked him. He then tied Aniruddha with the nagastra. Hearing this from Narada, Sri Krishna attacked Banasura's city with His army. To aid Banasura, Shiva gave him his armies and also came to support him in person, along with his children. Sri Krishna defeated them all and cut all but four of Banasura's thousand hands with His discus. He then pardoned Banasura due to the prayer of Shiva to spare him.

Ganga - This can be taken as Ganga's birth or Ganga and Shiva's birth. For the former, when Sriman Narayan measured the worlds as Trivikrama, His feet was washed by Brahma in satyaloka. That water fell to earth as Ganga which was accepted by Shiva on his head.

For the latter, Shiva was created by Brahma who was created by Sriman Narayana - "nAnmuganai nArAyaNan padaiththAn, nAnmuganum thAn mugamAych sankarnaith thAn padaiththAn".

nAma - Shiva getting his name from Brahma as well as based on his qualities.

samvAdana - There are many places in itihasas and puranas where others came to Shiva with their difficulties and he along with them went to Sriman Narayana to get those difficulties removed.

sva ukti - Shiva himself has said to Parvati and others about the supremacy of Narayana ("srIrAma rAma rAmeti").

ambarISha bhaya - King Ambarisha was a devout devotee of Sriman Narayana. One time, Durvasa maharishi came to his place on the morning of Dvadasi. The king had fasted the day before and was waiting to break it. The rishi went to the river and took a long time to return. So, the king broke the fast with a sip of water within the nominated time and waited for the rishi. When the rishi came and figured out what had happened, he became very angry with the king. He created a demon from his hair and sent it after the king. The king prayed to Sriman Narayana who sent His Sudarshana discus to the aid of the king. To escape the discus, the rishi surrendered to Shiva for help. Shiva could not do that. So the king surrendered to Sriman Narayana. He asked the rishi to obtain his pardon from the king himself. Durvasa maharishi did that and was saved.

shApa mukhai: - Shiva being cursed by Brahma for having cut one of Brahma's heads and having to beg alms in all worlds is a well known story. Azhvar too speaks of it as "piNdiyAr maNdai Endhi piRar manai thirithandhuNNum muNdiyAn sAbam".

Adi - Gaining protection by staying in His stomach during praLaya etc.