Data Sufficiency (DS) | Re: If x is a positive integer, is (x)(x + 2)(x + 4) div by 12?

Here's my interpretation, I'd actually love it if someone could tell me if I'm wrong here as I often make little mistakes in the theory on these questions.

Is (x)(x + 2)(x + 4) divisible by 12?

(1) x^2 + 2x is a multiple of 3.
(2) 3x is a multiple of 2.

I immediately rephrase the 12 into (2^2)*(3). So we need to be divisible by 2 twice and 3 one. So contained in these three terms we need two multiples of 2 and one multiple of 3.

First observation is we either have consecutive even numbers
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