The correct answer is option 4: "The old man told his grandson that he would teach him."

This option accurately reflects the change in tense and pronoun necessary when converting direct speech to reported speech. Let's break down why the other options are incorrect and why option 4 is the best choice:

• Option 1: This uses the past simple tense ("taught"), implying the teaching already happened. The original sentence uses the future simple tense ("will teach"), indicating a future action.
• Option 2: This changes the meaning entirely. The reported speech should reflect the old man's statement, not give an instruction to the grandson.
• Option 3: This retains the "will teach," which is incorrect when converting to reported speech. Reported speech requires a shift in tense.
• Option 4: This correctly changes "will teach" to "would teach," accurately reflecting the shift from future simple to conditional simple in reported speech. The pronoun "you" changes to "him," correctly representing the change in perspective from the direct speech to reported speech. This maintains the original meaning while adhering to grammatical rules for reported speech.

The core concept here is the correct usage of reported speech. Converting direct speech to reported speech involves shifting verb tenses, adjusting pronouns, and sometimes changing time and place references. In this particular case, the future tense ("will teach") must shift to the conditional tense ("would teach") to accurately reflect the statement within the context of reported speech. The pronoun "you" is changed to "him" because the grandson is now the recipient of the action described. This maintains the essence of the original message while adhering to the grammatical structure of indirect speech. Remember that the choice of tense is crucial for clarity and accuracy. The other options either incorrectly maintain the original tense, create a completely different meaning or fail to correctly represent the shift in perspective. Therefore option 4 best represents the original sentence in indirect speech.