Hi Render,

If this is the way the question was worded then I am not surprised you are confused. If the second sentence read

Then he cuts a second piece of rope that is 3/2 inches longer than the first piece.

then the second piece would be $12 + \large \frac{3}{2} \normalsize = 13 \large \frac{1}{2}$ inches long. However I don't think that is what is expected. I think you are expected to see the length of the second piece as $\large \frac32 \normalsize \times 12$ inches. If this is what is expected then the second sentence should have read

Then he cuts a second piece of rope that is 3/2 as long as the first piece.

or even clearer

Then he cuts a second piece of rope that is 3/2 times as long as than the first piece.

After you have completed the problem try it again with the fraction changes to $\large \frac{2}{3}$ and see how your answer changes.

I hope this helps. Write back if you need more assistance.
Penny