Just don't understand how to apply operation rules

Let ♥ be the operation defined by a ♥ b = 2b – 2a. Find 16 ♥ (8 ♥ 4).
Let ~ be the operation defined by a ~ b = 9-b/a+ab . Find –1 ~ 9
Let ♦ be the operation defined by a ♦ b = 5a – 7b. Find (2 ♦ 6) ♦7.

My son's teacher loves these types of problems and he just can't figure them out.
I would like to know if anyone can give just give me a place to start in helping him. I don't really understand them myself and he dosen't seem to be able to explain them to me. These are questions from already completed homework, so I have the answers but can't figure out the work.

Just plug the numbers into the formulas.

a) The "heart" operation says that x-heart-y means 2y - 2x. So, for instance, 3-heart-5 would be 2(5) - 2(3) = 10 - 6 = 4. To evaluate 16-heart-(8-heart-4), plug 8 and 4 into the "heart" formula, and then plug 16 and the result of 8-heart-4 into the "heart" formula.

b) The "tilde" operation says that x-tilde-y means (I am guessing) (9 - y)/(x + xy). So, for instance, 3-tilde-5 would be (9 - 5)/(3 + 3×5) = (4)/(3 + 15) = 4/18 = 2/9. To evaluate -1-tilde-9, plug -1 and 9 into the "tilde" formula.

c) The "diamond" operations says that x-diamond-y means 5x - 7y. So, for instance, 3-diamond-5 would be 5(3) - 7(5) = 15 - 35 = -20. To evaluate (2-diamond-6)-diamond-7, plug 2 and 6 into the "diamond" formula, and then plug this result and 7 into the "diamond" formula.

If you get stuck, please reply showing all of your steps and reasoning. Thank you.

Eliz.