Lord Narasimha is also called as Ashtamukha Gandaberunda. Remember, Pratyangira is not to be confused with the lion faced devi form, which seems like an extension of the dasha maha vidya. Here, Prtyangira or Simha Mukhi Lakshmi is none but Mahalakshmi.
It is believed that Ashta Mukha Gandaberunda is none but the combined power of Narasimha in all his Grandeur with Sharabha, Durga,Kali forming a part of his body and Lakshmi as Narasimhi/Pratyangira cooling his ferocity.
To establish dharma, save pious people from the clutches of demons / ill minded people, Sriman Narayana manifested into several avatars and Sri Narasimha Avatar is one among them; most of us knew that Narasimha had killed Hiranyakasyapu, the demon king and blessed Prahlada his great devotee; due to His furious nature as Narasimha, no one could control his anger, Brahma and other mini gods were afraid of his rage.
Brahma, accompanied by other mini gods, approached Shiva and described the Narasimha Avatar. Siva took it lightly and said this is a tiny issue and he can sort it out with ease in no time; he instructed Vinayaka to subdue Narasimha; when Vinayaka approached Narasimha, Narasimha severely warned and drove him away; Nandi, Aghora Veerabhadra were sent to subdue Narasimha, one after the other, after Vinayaka failed in his attempts, Nandi, Aghora Veerabhadra were severely attacked by Narasimha and they reported severity of their experience to Siva; ego and arrogance entered Shiva’s mind and he took the form of Sharabeswara with 5 heads, 16 arms, 8 legs, Kali and Durga as his wings and was accompanied by his parivara devatas and he reached the spot to fight with Narasimha.
Narasimha’s blazing fury reached peak, he took the form of Ashtamukha Gandabherunda Narasimha – the 8 faces are:
1] Twin headed Gandabherunda facing East,
2] Adi Jvala Narasimha facing SouthEast,
3] Vyagra facing South,
4] Hayagriva facing SouthWest,
5] Varaha facing West,
6] Hanuman facing NorthWest,
7] Garuda facing North and
8] Bhalluka facing NorthEast.
Here we have to note the power and secret of the name. Many of us knew very well that Hanuman also has 5 faces and in that form he is called / worshiped only as Panchamukha Hanuman but whereas here the name is Sri Ashtamukha Gandabherunda Narasimha and not Ashtamukha Gandabherunda. There is a significance of the name Narasimha added as suffix to the name i.e. all the 8 faces not only have their individual, specific grandeur and strength but it is combined form, i.e. gets double effect, fortified with the grandeur, strength of Narasimha and that is why this avatar gets the name as Sri Ashtamukha Gandabherunda Narasimha.