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To simplify the expression \(2(x+1)(x+2)\), we can start by expanding it step by step.
First, let's expand the binomials \((x+1)(x+2)\):
\[
(x+1)(x+2) = x^2 + 2x + x + 2 = x^2 + 3x + 2.
\]
Now, we multiply this result by 2:
\[
2(x^2 + 3x + 2) = 2x^2 + 6x + 4.
\]
Thus, the expression \(2(x+1)(x+2)\) can be written as \(2x^2 + 6x + 4\).
From the given options, the correct answer is:
**2x^2 + 6x + 4.**