"This is Teacher Wang's dad."
I'm new to Mandarin, but I'm pretty sure has to do with the word 老师 being the subject, and because you're not saying "this person", "this teacher", or "this pen". If it was 人 or an object (like apples) then you would need 个. It is a little tricky at first, but simple once you see it. You have to pay attention to the structure of the sentence. Good luck.
As I remember, my teacher taught us that 的 may be omitted when we indicate close relatives (妈妈，爸爸 and so on). Shouldn't this task have 2 correct answers (这是王老师的爸爸/这是王老师爸爸）or it may only refer to our close relatives, not to someone else's we are talking about at the moment?
In this case 的 can't be omitted, mainly due to "Teacher Wang's dad" being the object of the sentence and not the subject, but also because it sounds too familiar, being that either Wang is the teacher of the speaker or listener (or both), or "teacher" is the respectful title usage here, in which case Wang may not actually be a teacher but is definitely being respectfully addressed. In either case, "王老师爸爸" would be casual/familiar to the point of being rude.