Six more than the quotient of a number and 4 is 3

We presume you want to find the number.

Let n represent the number.
  6 + n/4 = 3 . . . . . . . 6 more than the quotient of a number and 4 is 3.
To solve this, we "undo" what is done to the number. First we undo the addition of 6 by adding its opposite, -6. We add -6 to both sides of the equation so the equal sign remains valid.
  6 -6 +n/4 = 3 -6
  n/4 = -3 . . . . . . . . simplify
Now, we need to undo the division by 4. We do that by multiplying by 4. Again, we must do that to both sides of the equation so the equal sign remains valid.
  4(n/4) = 4(-3)
  n(4/4) = -12
  n = -12

The number is -12.