The modulus of $ z $ is:
$$ |z| = 8$$To find modulus of a complex number $ z = a + bi $ we use formula:
$$ |z| = \sqrt{a^2 + b^2} $$In this example we have $ a = -4 \sqrt{ 3 } $ and $ b = 4 $ so:
$$ \begin{aligned}|z| &= \sqrt{ \left(-4 \sqrt{ 3 }\right)^2 + 4^2 } \\[1 em]|z| &= \sqrt{ 48 + 16 } \\[1 em]|z| &= \sqrt{ 64 } \\[1 em]|z| &= 8 \\[1 em] \end{aligned} $$