You can think of exponents as abbreviations for repeated multiplication. By that definition:
[tex] \big(\frac{6}{y}\big) ^3 =\frac{6}{y} \times\frac{6}{y} \times\frac{6}{y} [/tex]
Which, by the properties of fraction multiplication, is the same thing as
[tex] \frac{6\times6\times6}{y\times y\times y} [/tex]
whiiiich, going back to our abbreviations, is the same thing as
[tex] \frac{6^3}{y^3} [/tex]
And since 6³ = 216, our final simplified answer is
[tex] \frac{216}{y^3} [/tex]
The most important discovery in this problem is the property that
[tex] \big( \frac{x}{y}\big)^n=\frac{x^n}{y^n} [/tex]
You could almost say that the exponent gets "distributed" to the numerator and denominator, and in fact, any exponents will have this property of "distributing" across multiplication or division.
