Learn Spanish (Spain): El coche está sucio. Tengo que lavarlo.

We use está from the verb estar because being dirty is a temporary physical state or condition, not a permanent characteristic of the car. If you said es sucio, it would sound like the car is inherently a dirty type of object.

Why do we need the word que after tengo?

The phrase tener que followed by an infinitive verb like lavar is a special combination that means "to have to" do something. If you drop the que, the verb tengo just means "I have" in the sense of owning something.

Why is lo attached to the end of lavar to make lavarlo?

In Spanish, short object pronouns like lo (which means "it" here) can be attached directly to the end of an infinitive verb. Because tengo que and lavar work together as one idea, it is very common and natural to stick the pronoun on the end of the action verb.

Could I say lavarla instead of lavarlo?

Not in this sentence. The pronoun has to match the gender of the noun it replaces. Since el coche is a masculine noun, you must use the masculine pronoun lo. If you were talking about a bicycle (la bicicleta), then you would say lavarla.