#### Answer

$11\displaystyle \frac{31}{48}$

#### Work Step by Step

We combine the fractions by finding the LCD and simplify if necessary:
$12\displaystyle \frac{9}{16}-3\frac{1}{6}+2\frac{1}{4}=12\displaystyle \frac{27}{48}-3\frac{8}{48}+2\frac{12}{48} =9\displaystyle \frac{19}{48}+2\frac{12}{48}=11\displaystyle \frac{31}{48}$