Mr. White is playing with Mr. Green. They decided that stake of every round will be 50% of total money that Mr. Green has. Mr. Green said that he has in total 32$.
So in the first round stake was 16$. They played for 7 rounds and Mr. Green won 4 of them.
How much money Mr. Green has?
In my opinion Mr Green has just 40$ now and the order of winnigs have nothing to do with it because we have to do with geomtrical sequence here. He won 4 times loose 3 times.
You are correct that the order of wins and losses don't matter, though your answer is incorrect.
When Mr. Green wins he gets half of his current total back, or $1.5$ of his total as an end result. When he loses it's half the money, or $0.5$ of the total.
$$32\cdot1.5^4\cdot0.5^3=20.25$$