I'm planning to buy Pi 3, and I was wondering if can mount it to the back of my monitor with a VESA mount?
I know that many cases support mounting, but how can I know if a certain case is compatible with a VESA mount? I noticed that some cases have four holes or wall mounts on the back side, so I assume that's used for mounting?
A case that can be VESA mounted will probably be advertised as such.
I noticed that some cases have four holes or wall mounts on the back side
Yes, but those are unlikely to fit a VESA mount.
A quick look with a search engine at "raspberry pi vesa cases" reveals that the VESA spacing of the four screw holes looks broader than the base of the pi in most cases, hence the case has a bottom plate that extends beyond that. There are actually a set of possible dimensions, and a set of possible places on the monitor. Which one(s) your monitor uses is probably dependent on its weight.
Some cases refer to "75mm spacing". This is across; the long dimension on the board is 85 mm. The smallest VESA diagonal is 100mm. The diagonal of the board itself is about that, but of course it is not square. A common configuration for the VESA cases seems to be using two holes with 75mm spacing.
Having the mount holes on an exterior part of the case may be better since it would make getting it on and off the back of the monitor easy.
Anyway, you should investigate your monitor and go from there. You might as well then just use a search engine, since if a case is VESA compatible but not described as such it is a bit useless since you need to know compatible with what spacing.
