What kind of approach can be used to solve this specific problem? An easy one if possible.
I thought about the Inclusion-Exclusion Principle; I think using generating functions will be more difficult.
Given that the variables $x_i$ are natural numbers.
Find how many solutions exist for the equation:
$$x_1 + x_2 + x_3 + x_4 + x_5 + x_6 = 24$$
$$x_1 + x_2 + x_3 > x_4 + x_5 + x_6$$