Learn Turkish: Bu mümkün değil. - This is not possible.

You absolutely could use a verb with an inability suffix, such as olamaz (it cannot be). However, using the adjective mümkün (possible) with değil (not) is a very common, natural expression in Turkish for saying something is impossible, without needing an action verb at all.

Where is the word for "is" in this sentence?

In Turkish, there is no standalone verb for "to be" (am/is/are). For the "it" or "this" form in the present tense, the "is" is simply understood from the context. You could attach the suffix -dir to the end to make it değildir (it is a fact that it is not), but in everyday speech, it is usually left off.

If I want to say "This is possible," do I just drop the word değil?

Exactly! To make the sentence positive, you simply remove the negative word değil. Saying Bu mümkün perfectly translates to "This is possible."