Given grammar :

S --> A B | ϵ A --> a B B --> S b

Substituting B in A production and in S production ,we have :

S --> aSbSb | ϵ

which is the production of our interest as far as generation of strings is concerned as A does not produce any strings on its own as there is no terminating production in A..

So considering : S --> aSbSb | ϵ

After epsilon , minimal string generated : abb

Now we have 2 S's in the RHS of production , so we can substitute any of the 2 S's with epsilon or abb..So say first S is substituted with epsilon and second one with "abb" , we get the string generated : ababbb

If we do substitution other way , we get : aabbbb

So we can see that it need not be the case that all a's followed by b's which is twice the number of a's..But this is for sure that the number of b's is twice the number of a's..

Bt in that also strings like : abbbba , abbabb etc are not covered ..

Hence the description of the language that L = {a^{n} b^{2n} | n >= 0} or L = {strings belonging to Σ* | number of b's = twice the number of a's} is not true..

**All we can say is the language being generated is a proper subset of L = {strings belonging to Σ* such that number of b's = twice the number of a's} . **