Translation:The large comb is beside the toothbrush.
But "van" cannot be translated as "exists" in this case. It would if the sentence were "A fogkefe mellett egy nagy fésű van." In the original sentence the definite article before "nagy fésű" shows quite unequivocally that we are talking about a comb the existence of which is an already acknowledged fact. In other words, the sentence answers the question "hol van a nagy fésű?" and not "mi van a fogkefe mellett?". In just stating where the object in question is located any suitable verb should be accepted: "is", but also "lies", if one wants, for some reason, to point out that the comb is indeed lying and not, for instance, standing, that is, leaning against the inner wall of a cabinet, or hanging from a hook.