I'm thinking of a number. When I multiply by 6, add 8 to the result, and multiply by 1/3 of the result, I get -2. What is the number?

"I'm thinking of a number." $\rightarrow x$
"When I multiply by 6" $\rightarrow 6x$
"add 8 to the result" $\rightarrow 6x + 8$
"and multiply by $\frac{1}{3}$ of the result" $\rightarrow \frac{1}{3}(6x+8)$
"I get -2." $\rightarrow = -2$

So the equation is:

$$\frac{1}{3}(6x+8) = -2$$

Multiply both sides of the equation by 3 to eliminate the fraction:

$$3 \times \frac{1}{3}(6x+8) = -2 \times 3$$ $$6x+8 = -6$$

Subtract 8 from both sides of the equation:

$$6x = -6 - 8$$ $$6x = -14$$

Divide both sides by 6:

$$x = \frac{-14}{6}$$

Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2:

$$x = -\frac{7}{3}$$

The number is $-\frac{7}{3}$.