According to Wikipedia, the D3200 has a "Nikon F bayonet with AF contacts" lens mount, which is the same as on my D3400. So this lens will certainly "fit" your camera. The question you have to ask is whether you can benefit from AF-P autofocus. And here the answer is definitely NO.

https://www.nikonimgsupport.com/eu...

[...] Cameras that are not compatible with AF-P lenses [...] Digital SLR cameras [...] D3200 [...]

As already mentioned: it fits mechanically, but the autofocus doesn't work. So it's not really useful unless you want to focus exclusively manually.

For newer cameras, however, the lens is excellent: compared to its predecessors, the 55-200 and 55-300 lenses, the focusing, the image quality and sharpness, the quietness and the speed are worlds better, the lens is in a completely different league.

And by the way, AF can ALWAYS be switched off very easily: set the lever on the body (not on the lens) to M (on the larger Nikons), or set it to MF via the i-menu (on the smaller Nikons), done.

For the D3200, the older 55-200 and 55-300 lenses will work. If price, size and weight don't bother you, however, you should take a look at the AF-S 70-300 VR, which also works on FX (full-frame) Nikons, and is now available at a very reasonable price due to the release of its successor in the AF-P variant. This 70-300 is a bit bigger and heavier than the 55-x00 lenses, but it is also visibly better. Moreover, it can also be used on an FX body later on.

I wouldn't buy the lens again because you can't switch off the AF. But you always learn something new...

Yes, the lens fits the Nikon D3200.