To simplify the expression [tex]4 \sqrt{3}[/tex] as [tex](a^2 \sqrt{3}) \div 4[/tex], we need to solve for the value of [tex]a[/tex].

Given: [tex]4 \sqrt{3} = (a^2 \sqrt{3}) \div 4[/tex]

We can simplify the right side by canceling out the factor of [tex]\sqrt{3}[/tex] by dividing by 4:

[tex]\frac{4 \sqrt{3}}{4} = \frac{a^2 \sqrt{3}}{4}[/tex]
[tex]\sqrt{3} = \frac{a^2 \sqrt{3}}{4}[/tex]

Now, by comparing the coefficients on both sides:
[tex]a^2 = 4[/tex]

Taking the square root on both sides:
[tex]a = \sqrt{4}[/tex]
[tex]a = \pm 2[/tex]

Therefore, [tex]a = \pm 2[/tex] is the value that satisfies the given equation.