Choice A is the correct answer. To factor completely, always look for a Greatest Common Factor (GCF) first.

1. The coefficients are 2 and 6. The GCF is 2.
2. The variables are $x^2$ and $x$. The GCF is $x$.
3. Combine them: The total GCF is $2x$.
4. Divide each term by $2x$: $2x^2/2x = x$ and $6x/2x = 3$.

So, the factored form is $2x(x + 3)$.

Choice B is incorrect because $2x+6$ can still be factored further (divisible by 2). Choice C is incorrect because it leaves an $x$ inside that could be factored out. Choice D is incorrect because expanding $2x(x-3)$ gives $2x^2 - 6x$, which has the wrong sign.