"El coche de él"
"Su coche" is just as valid. But you can use "de él" to emphasise that it is the guy's car, since "su" can mean both his and her.
Although I am just a beginner at this I am pretty sure that my answer should have been valid. I put, 'the car is his' but it was incorrect as apparently, the right answer was, 'the car of his' which does not make any sense. I find this situation completely unfair as my answer should have been accepted. I will carry on sticking by this.
While it is apparent from the sentence that the car is indeed his, that's not what the sentence is saying. "De" means "of", not "is", so this phrase is lacking a verb (predicate). "The car of his" doesn't make much sense and should probably be "The car of him", but "His car" makes more sense than either of those.