The modulus of $ z $ is:
$$ |z| = 2 \sqrt{ 7 }$$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 $ and $ b = -2 \sqrt{ 3 } $ so:
$$ \begin{aligned}|z| &= \sqrt{ 4^2 + \left(-2 \sqrt{ 3 }\right)^2 } \\[1 em]|z| &= \sqrt{ 16 + 12 } \\[1 em]|z| &= \sqrt{ 28 } \\[1 em]|z| &= 2 \sqrt{ 7 } \\[1 em] \end{aligned} $$