I am thinking of a number. If you multiply my number by four, add - 4 to the product, and then take 1/3 of the sum, the result is - 6. Find my number.

1/3 ((x*4) + (-4)) = - 6

First multiply by 3 to get rid of the 1/3.

(x*4) + (-4) = - 18

Subtract - 4 from both sides to get 4x alone. (Subtracting a negative number is the same as adding the number)

4x = - 14

Now divide both sides by 4 to get x alone.

x = - 3.5