I think "Peter and Neha are both going to play" should also be accepted. It actually sounds more natural than the answer given

'Peter and Neha are both going to play' - this is also correct

"Peter and Neha are both going to play" is a better answer. "Peter and Neha both are going to play" is less idiomatic, at least in US English.

Not only US English 'are both going' is the natural syntactic order in English