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I attempted solving the problem named "the better choice".
So in game 1, the total number of possible outcomes will be 16. The probability of getting two heads and two tails will be 3/8. Therefore, the number of points earned will be 3*3/8=9/8.
Now, in game 2, the number 6 can arrive one,two or three time. The probability of six arriving at least once will be 1- probability of six not arriving at all which is 91/216. Therefore, the number of points earned will be 2*91/216= 91/108.
Clearly, 9/8 is greater than 91/109, hence game 1 is a better choice.
I have also attached pictures of my solution for better understanding.