Learn Turkish: Senin duvara asman gereken termometre burada yok. - The thermometer you must hang on the wall is not here.

This is a relative clause of necessity, which literally translates as "the thermometer which is necessary for your hanging". You combine the verbal noun asma (hanging) with the possessive suffix -n (your). You then add gereken (which is necessary) right before the noun it modifies (termometre).

Why is it duvara (to the wall) instead of duvarda (on the wall)?

In English, you hang something on a location. However, in Turkish, the verb asmak (to hang) focuses on the destination of the object being moved. Because it shows direction, it requires the dative case (-a/-e). That's why it is duvara asmak.

Is it mandatory to use the pronoun Senin at the beginning of the sentence?

No, it's optional. The suffix -n on asman already tells us who has to do the hanging (you). Adding Senin just gives extra emphasis, as if saying "The thermometer you are supposed to hang (and not someone else)."

How does this structure differ from saying duvara asacağın termometre?