The question requires you to find number of the outcomes in which at most 3 coins turn up as heads.
i.e., 0 coins turn heads or 1 coin turns head or 2 coins turn heads or 3 coins turn heads.
The number of outcomes in which 0 coins turn heads is 6C0 = 1 outcome
The number of outcomes in which 1 coin turns head is 6C1 = 6 outcomes
The number of outcomes in which 2 coins turn heads is 6C2 = 15 outcomes
The number of outcomes in which 3 coins turn heads is 6C0 = 20 outcomes.
Therefore, total number of outcomes =1+6+15+20= 42 outcomes.