List all possible license plate numbers

I would use

a = Alphabet[]; (* letter *)
d = Range[0, 9]; (* digit *)

result = Tuples[{a, a, d, d, d, d}];

you can definitely use Outer if you prefer

a = Alphabet[];
b = Range[0,9];
list = Flatten[Outer[List, a,a,b,b,b,b], 5];
list//Length
(* 6760000 *)

Just to show how this can be done using the OP's proposed approach:

Flatten[Outer[Join, letterCombinations, numberCombinations, 1], 1]

The other responses are ~ 10x faster.

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