Letter Combinations - Approach

Map each digit to its letters: $2 \to$ abc, $3 \to$ def, etc.

$1.$ For each digit, try each of its mapped letters.

$2.$ Recurse to the next digit.

$3.$ When all digits are processed, add the combination to results.

If there are $n$ digits with average $m$ letters each, you generate $O(m^n)$ combinations.