Question

tegumai did not speak to the stranger because he was busy rewrite the underlined word with modal auxiliary denoting obligation

Answer 1

The given sentence can be rewritten using the modal denoting obligation as shown below:

Tegumai did not speak to the stranger because he had to do something urgent/important/work.

Explanation

‘Have to’ is a modal verb that is used to show that you must do something. We also use ‘have to’ when the situation makes something that is necessary to be done.  The past tense form of 'have to' is 'had to'

Examples

I had to go for evening walk. (The doctor’s advice)

The students had to sit quietly in the class. (It was a rule)