Boozer
Drunkard
noun
We have alcohol and the noun form of 飲む (to drink). So you know this has to do with drinking alcohol. It means a boozer or a drunkard, someone who drinks a lot of alcohol!
酒飲み literally means "alcohol drinker," and it usually implies that the person consumes a lot of alcohol. This is a casual word and it can sound playful (like teasing a friend) or mildly critical depending on the situation and tone.
The readings are the vocab words お酒 and 飲む combined together into one. You can guess it's a kun'yomi reading because of the み on the end of 飲, which should make you think back to vocab words that use the kun'yomi readings for these kanji. If you can do that, you can read this word (and many others, probably)!
私の父親も酒飲みなんですよ。
My father is also a boozer.
コウイチはお酒は好きだけど、酒飲みってほどじゃあないですよ。
Koichi likes drinking, but he isn't like an alcoholic.
彼は大酒飲みだが、赤ワインが苦手だ。
He's a heavy drinker but he doesn't like red wine.