First of all, the probability of getting both coins to be heads is 1/4. You can see that this is true because there are four different possibilities (TT, TH, HT, and HH) and only one of them yields two heads, HH.
The probability for getting a 4 on a fair die is 1/6 because there are 6 numbers on a die and we assume that the probabilities for getting each one is the same. In probability questions where the two events x and y are independent (meaning the outcome of one does not affect the outcome of the other), when it asks for the probability of x and y, the "and" signifies that you multiply the probability of x with the probability of y. In our case, that is 1/4*1/6 = 1/24.