We are asked to multiply and simplify the expression $(\sqrt{7}-2\sqrt{3})^2$.

1. Problem Description

We are asked to multiply and simplify the expression $(\sqrt{7}-2\sqrt{3})^2$.

2. Solution Steps

We will use the formula $(a-b)^2 = a^2 - 2ab + b^2$.

Here, $a = \sqrt{7}$ and $b = 2\sqrt{3}$.

Then,

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

$= 7 - 4\sqrt{7\cdot3} + 4(3)$

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

$= 19 - 4\sqrt{21}$

3. Final Answer

$19-4\sqrt{21}$