Exegesis:

kai Pilatos epekrinen genesthai to aitēma autōn ‘and (consequently) Pilate decided that their request, i.e. what they requested, should be done.’

epikrinō ‘to decide,’ ‘to determine,’ not a specific judicial term.

aitēma ‘request,’ here referring to the content of the request.

Translation:

Gave sentence, or, ‘pronounced/passed sentence.’

That their demand should be granted, or, ‘that he (i.e. Pilate) would do what they asked for,’ ‘to comply with their request’ (Balinese, Tae’).

Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.