We factor the (9x2 − 16) into (3x + 4)(3x − 4) using the Difference of Squares that we learned before.
Dividing by (4 − 3x) is the same as multiplying by 1/(4 − 3x). (To see why, think about this example: dividing by 2 is the same as muiltiplying by 1/2.)
The second line involves the following useful trick:
(4 − 3x) = −(3x − 4)
(To see why this works, just multiply out the right hand side.)
After cancelling, we are left with a factor of (−1) from the cancelled fraction and this negative is placed out the front for convenience.