Lucky explained it right.
In probability there are two concepts (yes there are actually more, but for the purposes of this argument there are 2)
The two routes are OR and AND.
AND means you want two or more things to all happen together
OR means you want any of two or more things to happen
Self explanatory no?
So it's quite simple.
AND = multiply
OR = add
So if you want to know the chance of having one number AND the same number again on that die, you take the probability of the first (1/18) multiplied by the probability of the second condition (1/8). In this case, you just extend it out 3 more times.