If Greg rolls four fair six-sided dice, what is the probability that he rolls an equal number of 1's and 6's?

You mean "what is the probability of rolling 2 "ones" and 2 "sixes"?

The probability is: 4C2 * 2C2 =6 / 6^4 = 1 / 216

What about one 1 and one 6?

....and 3 ones and 3 sixes?