Question

An enrolling high school student has the following subjects to open to her:

Answer 1

So we notice that they increase by 1
each time
first slot we have all of them so
4 choices=1st slot
3 choices=2nd slot (1 was taken for 1st slot)
2 choices
1 choice
multiply
4 times 3 times 2 times 1=24
answe ris 24 ways
 

Answer 2

From the other answer, I see that my colleague with the busted clock
interpreted your question in a different way.  So I should explain
how I understand your question.

I understand you to say that both English sections meet at the
same time, all 3 math sections meet at the same time, all 3 History
sections meet at the same time, and all 4 Biology sections meet at
the same time.  So our student will take the subjects in that order,
but for each period, she can choose which section to join.
If that's not the right way to understand the question, then it's definitely
too complicated for me.

Reading it MY way,
here's the solution:

English: 2 choices.  For each of those . . .
Math:     3 choices.  For each of those . . .
History:  3 choices.  For each of those . . .
Biology:  4 choices.

Total possible different line-up of sections:

                     (2 x 3 x 3 x 4) = 72 different line-ups.