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.