Construct an automaton that recognizes the following language of strings over the alphabet {a,b}: {a,bb} that is only a and bb
Do anyone think that this might be the right approach or has any suggestion to somethin else.

Construct an automaton that recognizes the following language of strings over the alphabet {a,b}: {a,bb} that is only a and bb
Do anyone think that this might be the right approach or has any suggestion to somethin else.

Your NFA accepts only a language with a single word, namely $\{abb\}$. So you will need some branching in you automaton to fulfill your purpose.
Hint: Since the two words start differently, you need one branch for each.