The problem asks to simplify the expression $(\sqrt{7} - 2\sqrt{3})^2$.

1. Problem Description

The problem asks to simplify the expression $(\sqrt{7} - 2\sqrt{3})^2$.

2. Solution Steps

We can expand the expression using the formula $(a-b)^2 = a^2 - 2ab + b^2$. In this case, $a = \sqrt{7}$ and $b = 2\sqrt{3}$.

$(\sqrt{7} - 2\sqrt{3})^2 = (\sqrt{7})^2 - 2(\sqrt{7})(2\sqrt{3}) + (2\sqrt{3})^2$

$(\sqrt{7})^2 = 7$

$2(\sqrt{7})(2\sqrt{3}) = 4\sqrt{7 \cdot 3} = 4\sqrt{21}$

$(2\sqrt{3})^2 = 2^2 \cdot (\sqrt{3})^2 = 4 \cdot 3 = 12$

So, the expression becomes:

$7 - 4\sqrt{21} + 12$

Combining the constants:

$7 + 12 - 4\sqrt{21} = 19 - 4\sqrt{21}$

3. Final Answer

$19 - 4\sqrt{21}$