He told me that he----------- do this work
He told me that he----------- do this work
Explanation
The reported speech of the sentences past.
Therefore, the past perfect tense needs to be used as the name suggests past perfect tense is a part of the perfect tense and thus indicates completed actions.
in this case, "could" be used.
Subject( he) + had + Verb(could) (past participle) + object (this work).
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ND30-12-2022