Learn Swedish: Har du möjligtvis sett min kamera? - Have you possibly seen my camera?

We first take the neuter form möjligt and then add the suffix -vis. The suffix -vis works a lot like the English '-ly' or '-wise' to turn an adjective into a sentence adverb.

Why is there a -t- in the middle of möjligtvis?

The suffix -vis attaches to the neuter form of the adjective, which is möjligt. While you might hear people say möjligvis in fast casual speech, the correct written form includes the -t-.

Could I use kanske instead of möjligtvis in this sentence?

You could, but it changes the tone slightly. Kanske means 'maybe' and is a bit more direct. Möjligtvis translates to 'possibly' and makes the question sound much softer and more polite.

Why does möjligtvis go right after the subject du?

Möjligtvis is a sentence adverb, just like inte or ofta. In a main clause question, the first verb (har) comes first, followed by the subject (du), and then the sentence adverb always goes before the main verb (sett).