Simplify the expression $-6\sqrt{\frac{3y^2}{16}}$.

1. Problem Description

Simplify the expression $-6\sqrt{\frac{3y^2}{16}}$.

2. Solution Steps

We can rewrite the expression as:

$-6 \sqrt{\frac{3y^2}{16}}$

We can separate the square root of a fraction into the fraction of the square roots:

$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

Applying this, we have:

$-6 \frac{\sqrt{3y^2}}{\sqrt{16}}$

We can further separate the square root of a product into the product of the square roots:

$\sqrt{ab} = \sqrt{a} \sqrt{b}$

Applying this, we have:

$-6 \frac{\sqrt{3} \sqrt{y^2}}{\sqrt{16}}$

Since $\sqrt{y^2} = |y|$ and $\sqrt{16} = 4$, we have:

$-6 \frac{\sqrt{3}|y|}{4}$

We can simplify the fraction by dividing both the numerator and denominator by 2:

$-3 \frac{\sqrt{3}|y|}{2}$

Combining the constants, we have:

$-\frac{3\sqrt{3}}{2}|y|$

3. Final Answer

$-\frac{3\sqrt{3}}{2}|y|$