Is the first sentence correct? Does it have the same meaning as the second one?
- Him knowing four languages helped him with getting a job.
- The fact that he knows four languages helped him with getting a job.
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The first sentence is correct, and has the same meaning as the second one, but it is awkward. The one suggested by AlanCarmack (without "him") would be the preferable phrasing.
See also other questions tagged gerund-clause.
It's all a matter of what kind of English we're talking about here.
The first sentence is a possessive gerund. In formal English, I believe Him knowing is incorrect; it would be His knowing instead. But here's a person who says this kind of traditional grammar is "rubbish":
I don't necessarily agree with him. I think his knowing is a little more precise than him knowing. I guess I'm old-fashioned.