"Ce que" is correct, because "il" is the subject of the clause and "ce que" is the direct object. It belongs to the same clause whose verbe is "fait".
Tout ce qu'il fait m'agace. -- Everything he does annoys me.
Je trouve tout ce qu'il fait énervant. -- I find everything he does annoying.
In the first sentence "tout ce qu'il fait" is the subject of "m'agace". Whereas in the second sentence it is the direct object of "Je trouve". As you see, in both cases "ce que" is required because it is determined by its relationship to "il fait".
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