The number following the ^ is an exponent.

Recall three of the laws of exponents I assume your teacher must have covered in your class:

i) x^{m}x^{n} = x^{m+n}

ii) (x^{m})^{n} = x^{mn}

iii) (xy)^{n} = x^{n}y^{n}

These two laws can be used here:

y^{9}(2y^{2})^{3} = 2^{3}y^{9}y^{2*3} = 8y^{9}y^{6} = 8y^{9+6} = 8y^{15}