I would say yes.
In case of the four letter word with two letter alphabet, we have a choice of $2$ letter for each letter of the 4 letter word, and then consistent to rule of product we get $2\times 2 \times 2\times 2= 2^4$.
Note we are allowing repetition of letters of the alphabet in each case.
This problem is the reminiscent of the problem of finding the number of possible way of distributing $r$ distinct items into $n$ distinct groups where some groups could be empty.
Other ways to model this same problem:
$(1)$ Number of ways of drawing a sample of $r$ objects from a set of
$n$ distinct object when order of drawing is important and we allow
$(2)$ Distributing $r$ distinct balls into $n$ distinct cells with any
number of balls per cell.
However,the answer in all these cases is $n^r$, which is again consistent to the rule of product.