There are $2^4=16$ possible outcomes, since each of the 4 coins can land 2 different ways (heads or tails). There are 2 possibilities for the dime and 2 for the quarter, so there are $2 \times 2 = 4$ successful outcomes, and the probability of this is $\dfrac{4}{16} = \dfrac{1}{4}$.
Suppose we flip four coins simultaneously: a penny, a nickel, a dime, and a quarter.  What is the probability that the penny and nickel both come up heads?