Final answer:
The word that means 'to strongly encourage' and contains all the letters in the word 'encourage' is 'a) Urge'.
Step-by-step explanation:
The word that means 'to strongly encourage' and contains all the letters in the word 'encourage' is a) Urge. The word 'urge' not only has all the letters from 'encourage', but it also carries the meaning of strong encouragement or a strong desire to do something. For example, you could say, 'I urge you to study for your exams' which means 'I strongly encourage you to study for your exams'.