Learn Russian: Это тот автомобиль, которому нужно настроить глушитель. - This is the car that needs its muffler tuned.

In Russian, the car is not the direct subject or object of the verb here. Instead, it acts as the indirect beneficiary or target of the action. You are tuning the muffler for or to the car, so автомобиль (represented by которому) takes the Dative case. A literal translation would be 'This is that car, to which it is necessary to tune the muffler.'

What case is глушитель in, and why?

It is in the Accusative case because it is the direct object of the verb настроить (to tune). Since глушитель (muffler) is an inanimate masculine noun, its Accusative form looks exactly identical to its Nominative dictionary form.

Why do we need the word тот (that) in the first half of the sentence? Couldn't we just say Это автомобиль, которому...?

While you could just say Это автомобиль, using the demonstrative pronoun тот (that/the) makes the sentence much more natural. It acts as a pointer to the relative clause которому..., functioning like 'the specific one' in English. This тот ..., который ... structure is very common in Russian when you want to single out an exact item.

Could we use настраивать (imperfective) instead of настроить (perfective) here?