Chapter 6 - Radical Functions and Rational Exponents - 6-3 Binomial Radical Expressions - Practice and Problem-Solving Exercises - Page 378: 30

$4$

Using the product of the sum and difference of like terms which is given by $(a+b)(a-b)=a^2-b^2,$ the given expression, $ (4-2\sqrt{3})(4+2\sqrt{3}) ,$ is equivalent to \begin{align*} & (4)^2-(2\sqrt{3})^2 \\&= 16-4(3) \\&= 16-12 \\&= 4 .\end{align*}