#### Answer

$ b=2$

#### Work Step by Step

If the solution set is $\{-6\}$, by substituting $ x=-6$ into the equation, it should be true.
$\displaystyle \frac{7(-6)+4}{b}+13=-6\qquad $ ... we now solve this for b
... subtract 13
$\displaystyle \frac{-38}{b}=-19\qquad $ ... multiply with b
$-38=-19b\qquad $ ... divide with $-19$
$ b=2$