The problem asks to simplify the expression $\sqrt{12} + \sqrt{75} - 2\sqrt{108}$.

1. Problem Description

The problem asks to simplify the expression $\sqrt{12} + \sqrt{75} - 2\sqrt{108}$.

2. Solution Steps

First, simplify each radical term:

$\sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}$

$\sqrt{75} = \sqrt{25 \cdot 3} = \sqrt{25} \cdot \sqrt{3} = 5\sqrt{3}$

$\sqrt{108} = \sqrt{36 \cdot 3} = \sqrt{36} \cdot \sqrt{3} = 6\sqrt{3}$

Substitute the simplified radicals back into the original expression:

$\sqrt{12} + \sqrt{75} - 2\sqrt{108} = 2\sqrt{3} + 5\sqrt{3} - 2(6\sqrt{3})$

$= 2\sqrt{3} + 5\sqrt{3} - 12\sqrt{3}$

Combine the terms with $\sqrt{3}$:

$= (2 + 5 - 12)\sqrt{3}$

$= (7 - 12)\sqrt{3}$

$= -5\sqrt{3}$

3. Final Answer

The final answer is $-5\sqrt{3}$.