Exegesis:

hoi de epekeinto … aitoumenoi ‘but they persisted in demanding.’ For epikeimai cf. on 5.1; here it is used of applying mental pressure, with following participial clause indicating what was pressed for, i.e. that Jesus should be crucified.

phōnais megalais ‘with loud voices,’ elsewhere in the singular (cf. 19.37), in a clause with plural subject, here in the plural, without difference in meaning.

katischuon hai phōnai autōn ‘their voices, i.e. their shouting prevailed.’

katischuō here ‘to prevail,’ ‘to win the day.’

Translation:

They were urgent, demanding, or, ‘they insisted on their demand,’ ‘they pressed (lit. made to walk) their earnest entreaty’ (Marathi), ‘they kept on demanding,’ cf. “they kept on shouting” (Good News Translation, choosing a verb more in tune with the next phrase). The person to whom the demand is addressed may have to be indicated, cf. e.g. ‘they pressed him (or, Pilate) and asked,’ or, shifting the main verb, ‘they demanded him/Pilate urgently.’

With loud cries, or, ‘shouts,’ ‘crying/shouting loudly.’ The phrase may better become the main clause, cf. e.g. ‘they made-loud (lit. blazing) their voice to press him, asking’ (Batak Toba).

That he should be crucified, or, ‘that he (i.e. Pilate) should crucify him/Jesus, or, should have him/Jesus crucified.’

Their voices prevailed, or, ‘won-the-victory’ (Pohnpeian), is variously rendered, cf. e.g. ‘their noises defeated him’ (Fulah), ‘their words conquered, or, were obeyed’ (cf. Shona 1963, Tzeltal), ‘their voices made authority’ (Zarma, an idiom for a pronouncement one is forced to obey whether right or wrong), ‘success came to their yelling’ (Marathi), ‘they won-out’ (Kituba).

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.