The quotient of two fraction is the multiplication between the first and the inverse of the second:
[tex] \dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a}{b} \cdot \dfrac{d}{c} [/tex]
So, in your case, you have
[tex] \dfrac{3}{5} \div \dfrac{6}{7} = \dfrac{3}{5} \cdot \dfrac{7}{6} = \dfrac{7}{10} [/tex]
So, the question now is: which is larger, 7/10 or 3/5? To answer this question, transform the second fraction so that it will have denominator 10 as well:
[tex] \dfrac{3}{5} = \dfrac{3\cdot 2}{5 \cdot 2} = \dfrac{6}{10} [/tex]
So, now it is clear that
[tex] \dfrac{7}{10} > \dfrac{6}{10} [/tex]
