Explanation:

- A third proportional refers to a value "z" in the proportion A:B::B:z.

- Given are 3x² (A) and 4xy (B). The third proportional (z) is 48.

- Set up the proportion as 3x² : 4xy = 4xy : 48.

- Cross-multiply to get:

$$(3x²)\ast (48)=(4xy)\ast (4xy).$$

- Simplify:

$$144x²=16x²y².$$

- Divide both sides by 16x²:

$$9=y².$$

- Solve for y:

$$y=3\text{ or }y=-3.$$

- The positive value of y is 3.

Answer: Option 1: 3