Um... no....

You can only cancel factors, not terms or parts of terms. To learn how to simplify rational expressions, tryhere.

Then I made h = 0 and that got rid of the 4x^2h and left the x

Try using one of the techniques they showed you in your book and / or in your classroom lecture: noting that the numerator does not factor, instead divide everything by h:

. . . . .

. . . . .

. . . . .

. . . . .

Now there is no "division by zero" problem, so you can simply evaluate at h = 0, thus confirming the book's answer.