Let's let M = the number of Multiple choice problems and
N = the number of essay questions.
Since the multiple choice problems are worth 2 points and the essay questions are worth 6 points and the total number of points possible is 100, then:
2M + 6N = 100
Also, since there are 36 questions altogether, we can say that
M + N = 36
M = 36 - N
Now substitute M = 36 - N into the 1st equation above.
2(36 - N) + 6N = 100
72 - 2N + 6N = 100
4N = 100 - 72
4N = 28
N = 7
Now, since M = 36 - N, we can find that
M = 36 - 7 = 29
So the number of multiple choice problems is 29 and the number of essay questions is 7.
Now, check your answer:
2(29) + 6(7) = 58 + 42 = 100
The answer is correct.
For part b:
If the multiple choice problems are worth 4 points each and there are 29 multiple choice problems, then there would be 116 total points so it would not be possible.