To solve this problem, we need to follow the order of operations, which is also known as PEMDAS (parentheses, exponents, multiplication/division, addition/subtraction).

First, we need to evaluate the division inside the parentheses: 72 ÷ 4 equals 18.

Now, the problem becomes 18 ÷ (-6).

Finally, we divide 18 by -6: 18 ÷ (-6) equals -3.

Therefore, the quotient of 72 ÷ (4) ÷ (-6) is -3.