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(a) If we have no restrictions, its $\dbinom{28}{7}$

(b) If we need to have each sex proportionally represented: Is it possibly so that the answer is $\dbinom{12}{4}$$\dbinom{12}{3}$

(c) If we need to have at least on of each sex $\dbinom{16}{1}$$\dbinom{12}{1}$ $\dbinom{26}{5}$

(d) If the group should be either only men or only women Here I am thinking that $\dbinom{16}{7}$$\dbinom{12}{7}$

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    If by "proportionally represented" it means a quarter of both the males and a quarter of the females should be in the chosen group, then yes for both (a) and (b). For (c) and (d) however you have run into mistakes. It is easier to calculate (d) first and use that result to calculate (c) since (c) is the opposite of (d) and (d) is easier. To calculate (d), should you really have used multiplication? No? What else should you have done instead? – 2017-01-27
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    Remember your [rule of sum](https://en.wikipedia.org/wiki/Rule_of_sum)(*addition principle*) and [rule of product](https://en.wikipedia.org/wiki/Rule_of_product)(*multiplication principle*) and when it is appropriate to add versus multiply. – 2017-01-27

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Your answer to (d) is not correct: it should be $$\binom{16}{7} + \binom{12}{7},$$ because the choice of an all-male group is exclusive of the choice of an all-female group. Therefore, the number of such choices is the sum, not the product, of the number of choices within each sex.

For a simpler example, suppose I have $3$ red balls labeled $R_1, R_2, R_3$ and $2$ blue balls labeled $B_1, B_2$. How many ways can I choose $2$ balls of the same color? There are $\binom{3}{2} = 3$ ways to choose two red balls. There is only $\binom{2}{2} = 1$ way to choose two blue balls. There should be $3 + 1 = 4$ ways to get two balls of the same color.

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    If you are going to post, you should comment as well on the incorrectness of part (c). – 2017-01-27
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    @JMoravitz Why *should* I? There is no rule that says if I choose to comment on one part of the question, that I must also provide a complete solution to other parts or even suggest a correction. – 2017-01-27