[erlang-questions] why does the guard not working

[Richard A. O'Keefe]

You were using display_numbers_loop/1 to print all integers between 1 and N.
Now you are using the same name for printing EVEN integers between 1 and N.
It would be very helpful to change the name.

In order to print even numbers in a range, you are generating ALL integers
in that range, and then throwing away the ones you do not want.

Fine, in that case

    display_numbers_loop(N, N) ->
        ok;
    display_numbers_loop(N0, N) ->
        N1 = N0 + 1,
        case N1 rem 2
          of 0 -> io:format("Number: ~p~n", [N1])
           ; 1 -> skip
        end,
        display_numbers_loop(N1, N).

is the smallest change to your display_numbers_loop that will skip the
numbers you do not want.

But what's better still is not to generate the numbers you don't want
in the first place.