Learn Spanish (Latin America): Tienes que peinarte ahora.

Because peinar is an infinitive (a verb in its basic, unconjugated form). When you have a conjugated verb (tienes) followed by an infinitive, you can attach the reflexive pronoun right to the end of that infinitive to make one word: peinarte. You are also allowed to put the pronoun before the conjugated verb (Te tienes que peinar), but attaching it to the end is extremely common!

Where is the word for "hair" in the Spanish sentence?

It isn't there! In English we say "comb your hair," but in Spanish, personal grooming actions usually use reflexive verbs. Peinarse literally means "to comb oneself." Since the te already means "yourself," Spanish speakers don't need to add the word for hair—it's already understood!

Why is the word que in this sentence? Doesn't tienes already mean "you have"?

By itself, tienes does mean "you have" (like owning something). However, when you put que right after it, it creates the phrase tener que, which means "to have to" or "must" do something. So tienes que tells us about an obligation: "you have to."