Answer
$(-2,6)$.
Work Step by Step
The domain requirement for $f(x)=ln(\frac{-3}{(x+2)(x-6)})$ is $\frac{-3}{(x+2)(x-6)}\gt0$ or $(x+2)(x-6)\lt0$ which gives $-2\lt x\lt 6$ (one factor is negative), in interval notation $(-2,6)$.
Precalculus (6th Edition)
by Lial, Margaret L.; Hornsby, John; Schneider, David I.; Daniels, Callie
Published by
Pearson
ISBN 10:
013421742X
ISBN 13:
978-0-13421-742-0
Chapter 4 - Inverse, Exponential, and Logarithmic Functions - Summary Exercises on Functions: Domains and Defining Equations - Exercises - Page 487: 39
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