Acollege freshman must take a science course ,humanities course, and a mathematics course. if she ay select any of 6 science courses, any of 4 humanities courses, and any 4 mathematics courses. how many ways can she arrange her problem?

96 ways

In this case, the freshman must take one class each from Science(6 courses), Humanities(4 courses) and Mathematics( 4 courses).
Then to know how many ways she can arrange you just need to multiply the each course count (it would different if she has to take more than one class).
The calculation would be: 6 x 4 x 4= 96 ways.