。
Actually, this is my fourth time asking.
Literal
Actually this [with-で] 4-[ordinal-度目] [attributive-の] question become-[polite-ます].
実は ('actually, to tell the truth') is a common sentence opener for revealing something. ~度目 is the ordinal counter for 'the Nth time' — 度 is a time-counter, and 目 is the ordinal-marker suffix (as in 二番目, 'the second'). これで ('with this') marks the current instance as the one bringing the total to four. ~になる ('becomes X') is used for reaching states or tallies.