Hello,

The hint is here to let you know if you've forgotten any element.

We know that the empty set and omega belong to the sigma-field. That makes 2.

{1,3,5} and {1,2,3} obviously belong to the sigma-field, since they generate it.

We know a sigma-field is closed under union. So {1,3,5} U {1,2,3}={1,2,3,5} belong to the sigma-field.

Then we know it's closed under the complement : find the complement of {1,3,5}, {1,2,3} and {1,2,3,5} in Omega : {2,4,6}, {4,5,6}, {4,6}. That makes 3 more.

But now you can also do {1,3,5} U {4,5,6}={1,3,4,5,6} and its complement {2}

{1,2,3} U {2,4,6}={1,2,3,4,6} and its complement {5}

{2,4,6} U {4,5,6}={2,4,5,6} and its complement {1,3}

And the remaining union : {2} U {5}={2,5} and its complement {1,3,4,6}

That makes 16=2^4

You have to try finding all the possibilities...