Hello,
The fractions 4/6 and 6/9 are not in its simplest form, therefore we need to simplify both fractions.
For the fraction 4/6- both the 4 and 6 are divisible by 2, so if you divide the numerator 4 by 2, and the denominator 6 by 2, the fraction reduced is 2/3.
For the fraction 6/9- both the 6 and the 9 are divisible by 3, so if you divide the numerator 6 by 3, and the denominator 9 by 3, the fraction reduced is 2/3.
So in conclusion, yes- the ratio 4/6 and 6/9 are equivalent.
Hope this helps!
May