This image is of Karttikeya, a deity particularly popular in South India, and also known as Shanmuhka, Murugan, Skanda, Kumara, Subrahmanya, and by several other names.
Generally he is believed to be the son of Shiva and Parvati and so the brother of Ganesha, and in this manifestation is regarded as a god of war. In many Shaivite temples his images are employed as guardian deities.
In this image he is shown with six heads and twelve arms. The principal hands display the gestures of charity and fearlessness. The other ten radiating hands hold various attributes including a lotus, a shield, a thunderbolt, and a conch.
He sits in lalitasana pose astride his vahana or celestial mode of transport, the peacock.
The peacock stands atop o lotus pedestal, and has a prominent tail. From its beak dangles a double-twisted snake.
The image has a deep chocolate brown patina. Images of Karttikeya are relatively rare.
References
Pal, P., Art from the Indian Subcontinent: Asian Art at the Norton Simon Museum,Yale University Press, 2003.