The player has $5000 and if he play and the coin falls head he win $1000, and he plays 6 times . Now
Assuming that wen he loses he has to pay $1000, beacuse if we don't know how much he loses the exercise would be incomplete.
if he wins 0 and loses 6 he loses $6000, so will go with $0
if he wins 1 and loses 5 he loses $4000, so he will go with $1000
if he wins 2 and loses 4 he loses $2000, so he will go with $3000
if he wins 3 and loses 3 he loses $0, so he will go with $5000
if he wins 4 and loses 2 he wins $2000 so he will go with $ 7000
if he wins 5 and loses 1 he wins $4000 so he will go with $9000
if he wins 6 and loses 0 he wins $6000 so he will go with $11000
so in neither case he wins $6000 then the probability is 0. The answer is 0
Now if we assume that he doesn't lose money of that, the loses is not relevant we only need that he wins one time, the other ones doesn't matter. So we are looking of the probability that the coin falls head six times this is 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/(2^6) = 1/64. So the probability is 1/64