4 ÷ 6/9 is also equal to 4 x 9/6. This is because when you divide by a fraction, you change the division sign to multiply and reverse the numerator and the denominator of the fraction. For example, if x/y was a fraction, it would become y/x. THIS IS ONLY DURING DIVISION!
So, we now that 4 ÷ 6/9 is equal to 4 x 9/6. 4 x 9/6 = (4x9)/6 = 36/6 = 6.