You have the information at the end. The ratio is 4:7, and the difference is 72. This means that 3 units is 72 cards, and makes the total number of cards be 264

Since the total number of cards doesnt change, it is the same when the ratio is 3:1. You can work out how many 3 units is, which is 198 cards

Since he gave her 1/10 before, he now has 198 cards. This means that 198 cards is 9/10 of what he had. From there, you can work out how many he had at first, which is 220.

The total is 264. He had 220 at the start, hence she has 264-220 which is 44. The ratio is 220:44 that is 5:1

You can now calculate how many cards each person has at every trade. You find the difference from the start to the end and you can find how many she won from him. You should get 124 cards

Hope it helps!