The given expression is:
[tex]2\sqrt{x+2}\times\sqrt{x+3}[/tex]To evaluate the given expression, we apply the rule:
[tex]\begin{gathered} \sqrt{a}\times\sqrt{b}=\sqrt{ab} \\ 2=\sqrt{4} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} 2\sqrt{x+2}\times\sqrt{x+3} \\ =\sqrt{4(x+2)(x+3)} \\ =\sqrt{4(x^2+2x+3x+6)} \\ =\sqrt{4(x^2+5x+6)} \\ =\sqrt{4x^2+20x+24} \end{gathered}[/tex]