Sneak is a verb. Although it can be transitive, which means to "steal" something (usually just play some bad joke, I snuck a bug in the girl's bag), let's say, apparently it's INtransitive here, since you can't sneak the window into a girl's bag. Hope you're clear about that so far. So then "out" is the adverb, not a preposition here. That's pretty basic grammar stuff. Then you'll have to need a preposition to make the sentence make sense. ie, to connect an intransitive verb and its object. Therefore you could choose "of", or like Eliot, "through". It's NOT about British or Americanglish, it's only a grammar situation. Why the people think it's also correct without the "of" is that, you might be familiar with this, "outta", in colloquial speech, if you're as lazy as anyone else, you'll say, "let's get outta here", "sneak outta the window", which EFFECTIVELY, sounds the same as "get out here", but just because people are too lazy to pronounce every word distinctively doesn't mean you could have an alternative in grammar, in written formal English, there's only one correct choice, British or American, you don't forget "of". ps Something that might confuse you is, "she's still out t/here", ie the "out there", you don't need "of" here because "t/here" is not a noun like "get out of here", but an adverb like "I don't need you here".

Actually, it's: "Sneak out through the window." The verb is "sneak out". You could say: Sneak out out of the window.

I agree with David. Yet "Sneak out the window" would be more correct if you were stealing a window. :)

both are ok. 'sneaks out the window' would be more common in spoken english and 'sneaks out of the window' more common in written english

'Ot of the window' is correct in British English, 'out the window' is correct in American English, but may be becoming more common in Britain.