Why does Radix sort require stable digit sorts?
Integers that are equal in some digit aren't always equal (e.g., 12 and 13).

Let's sort [13, 12] using a LSD-first radix sort (base 10). But we'll use an unstable sort for each digit.

First we sort by the 1's place, so the array becomes [12, 13].

Now we sort by the 10's places, but 12 and 13 have the same digit. Since the sort is unstable, the resulting array could be [12, 13] or [13, 12]. We don't know.

If the sort were stable we would be guaranteed to get a correctly sorted array.