Translation:I cannot skateboard today because I have a lot of homework.
Because - 기 때문에 or just 때문에?
The thing that comes before 때문에 must be a noun. "Because of [something]".
So that "something" can either be just a regular old noun. "Because of you" = "너 때문에" (negative connotation)
Or, it can be a verb. If it's being used with a verb (like this sentence), you must "nominalize" the verb to make it into a noun. You have probably seen 는 것 before. 기 is essentially the same thing. It changes a verb into a noun form. So, "because he eats" = "그가 먹기 때문에".
In this example, a verb is used, being 많다. So simply change the verb to its noun form: 많다 -> 많기, then add 때문에. 숙제가 많기 때문에 = Because I have a lot of homework / Because there is a lot of homework.
If you simply wanted to say, "Because of homework", then you wouldn't need to nominalize anything. It would just be 숙제 때문에.
Yes, it is on occasion. It's not used very often (due to the lack of people skateboarding anymore) but it is a verb.
That's the noun form of the (descriptive) verb 많다. Descriptive verbs are the Korean equivalent of adjectives but they act like verbs in the sentence, hence the name.
As far as I kniw, word proceeding '때문에' must be a noun. No fixed forms here, you just have to be careful about that.
건강 때문에, 학교 때문에, 먹는 것 때문에, 많기 때문에 - those are OK
않이 때문에, 먹다 때문에 - wrong because an andverb and a verb are used here.
I'm confused as to why 많이 is being written as 많기. How does this form change the grammar?