How Do I Show That If F(n)=O(n2),g(n)=O(n3) That F(n)+g(n)=O(n3)?

Are you sure that's not

f(n) + g(n) = O(n5)?

As that's what I would have thought, and some people's written 3s can look like 5s, so maybe the worksheet problem you've been set is wrong.

The example looks like a chemistry problem.  So I am assuming the example O(n2) really means O * n(subscript 2).  That means "2 of substance n", so adding 2 of them to 3 of them would still suggest n (subscript 5) -- five of item n.

Show what I'm saying with

f(n) = O(n2)= O * (n + n).
g(n) = O(n3) = O * ( n + n + n).

f(n) + g(n) = O * n2 + O * n3 = O (n2 + n3) = O (n + n + n + n + n ) = O(n5).

Of course, the 2 and 3 in f(n) and g(n) could be superscripts -- ^ -- "raised to the power of".  Basic algebra stuff.
  But that would make the supposed answer even more impossible to work out.