The probability of exactly two heads when a fair coin is tossed 6 times is?

This is a binomial distribution; number of trials (n) is 6, probability of success (p) is 1/2 or 0.5. With this information you can go to a Binomial Distribution Table and find the solution. Within the section of values for n=6 and p=.5, read from the section the probability of 2 which is 0.2344 (see related link for table).