The problem is to divide the polynomial expression $\frac{3}{8}a^2b^2$ by $\frac{1}{4}y^2$. The expression "entre" suggests a division operation.

1. Problem Description

The problem is to divide the polynomial expression $\frac{3}{8}a^2b^2$ by $\frac{1}{4}y^2$. The expression "entre" suggests a division operation.

2. Solution Steps

We are asked to evaluate the expression $\frac{3}{8}a^2b^2 \div \frac{1}{4}y^2$. This is equivalent to multiplying $\frac{3}{8}a^2b^2$ by the reciprocal of $\frac{1}{4}y^2$. The reciprocal of $\frac{1}{4}y^2$ is $\frac{4}{y^2}$.

Thus, we have:

$\frac{3}{8}a^2b^2 \div \frac{1}{4}y^2 = \frac{3}{8}a^2b^2 \times \frac{4}{y^2}$

We can simplify the fraction by multiplying:

$\frac{3}{8}a^2b^2 \times \frac{4}{y^2} = \frac{3 \times 4}{8} \frac{a^2b^2}{y^2}$

Simplify the numerical coefficient:

$\frac{3 \times 4}{8} = \frac{12}{8} = \frac{3}{2}$

So, the result is:

$\frac{3}{2} \frac{a^2b^2}{y^2}$

Or, equivalently,

$\frac{3a^2b^2}{2y^2}$

3. Final Answer

The final answer is $\frac{3a^2b^2}{2y^2}$.