#### Answer

$= \frac{1}{24}$

#### Work Step by Step

1. Follow the acronym PEDMAS:
P: arenthesis
E: ponents
D:ivision
M:ultiplication
A:ddition
S:ubtraction
$= $ P.E.D.M.A.S
This is used to determine which order of operations is completed first from top to bottom. For example, you would complete the division of two numbers before the addition of another two numbers. In this case, we multiply and divide before adding and subtracting.
Note: We never can divide by a fraction, so instead of dividing, we multiply by the reciprocal of the fraction:
$\frac{1}{6} + \frac{2}{3} \times \frac{3}{4} - \frac{5}{6} \div \frac{8}{6}$
$= \frac{1}{6} + \frac{6}{12} - \frac{5}{6} \times \frac{6}{8}$
$= \frac{1}{6} + \frac{6}{12} - \frac{30}{48}$
2. Find a common denominator when adding and subtracting: In order to obtain a common denominator of $48$, we only have to multiply the first fraction by $8/8$ and the second fraction by $4/4$.
$= \frac{8}{48} + \frac{24}{48} - \frac{30}{48}$
$= \frac{32}{48}- \frac{30}{48}$
3. Finally we simplify the fraction:
$= \frac{2}{48}$
$= \frac{1}{24}$