Albert Barnes on Philemon 1:22

But withal. Or, at the same time-- αμα. While you are granting this favour, do me also another by preparing a lodging for me.

Prepare me also a lodging. Philemon had been accustomed to show kindness to the saints (Phm 1:6,) and not improbably Paul had before shared his hospitality. The word rendered lodging (ξενια) means, properly, guest-right, hospitality, entertainment; and then, a place for a guest. Compare Acts 28:23.

For I trust. Paul had some hope of being released--an event which probably occurred. Php 1:25; Php 2:23, Php 2:24. Compare Introduction to 2Ti 1:1

Through your prayers. 2Cor 1:11. He expected release in answer to the petitions of those who loved him, and the cause in which he was engaged. Compare Acts 12:5.

I shall be given unto you. I shall be permitted to return to you, as a favour χαρισθησομαι. Paul had no doubt that Philemon would so regard it, and he had no apprehension that his abiding with him would be considered as a burden.

(++) "withal" "At the same time" (c) "I trust" Php 2:24 (d) "through your prayers" 2Cor 1:11