What is the quotient of 4 and a number x increased by 6?

The expression for the quotient of 4 and a number x increased by 6 is (4/x) + 6. To simplify this expression, you would first divide 4 by x to get 4/x, then add 6 to the result. The final expression represents the quotient of 4 and x with an additional 6 added to it.