The correct option is C hopeful
Option C is correct because the suffix '-ful' forms the adjective meaning 'full of hope'. In "She felt optimistic, hearing the hopeful words he spoke regarding her treatment", the adjective 'hopeful' modifies the noun 'words' meaning, his words were full of hope. 'Hopeable', 'hopen' and 'hopely' do not exist in the dictionary. They're not used in Standard English, hence options A, B and D are incorrect.