Albert Barnes Commentary Acts 10:29

"wherefore also I came without gainsaying, when I was sent for. I ask therefore with what intent ye sent for me." — Acts 10:29 (ASV)

Without disputing. Without saying anything against it; without hesitation or reluctance.

I ask therefore, etc. The main purpose for which Cornelius had sent for him had been mentioned to Peter by the messenger (Acts 10:22). But Peter now desired from his own lips a more detailed statement of the reasons that had led him to send for him.

For what intent. For what purpose or reason.

"Intent" may also be understood as "on what account."