1. "I cannot run as fast as my dog does," said Henry.

• The original sentence is in the present simple ("cannot run") and uses "does" for the comparison.

• When converting to indirect speech, the present simple usually changes to the past simple ("could not run"). The "does" in the comparison also changes to "did".

• A. Henry told that he cannot run as fast as his dog does. (Incorrect - "cannot" and "does" should change to the past tense)

• B. Henry said that he couldn't run as fast as his dog does. (Incorrect - "does" should change to "did")

• C. Henry told that he cannot run as fast as his dog did. (Incorrect - "cannot" should change to "could not")

• D. Henry said that he couldn't run as fast as his dog did. (Correct - "cannot run" becomes "couldn't run", and "does" becomes "did")

Therefore, the correct answer for question 1 is D.

2. "I have been writing this letter for 2 hours," said Mike.

• The original sentence is in the present perfect continuous ("have been writing").

• When converting to indirect speech, the present perfect continuous usually changes to the past perfect continuous ("had been writing").

• A. Mike said that he has been writing that letter for 2 hours. (Incorrect - "has been" should change to "had been")

• B. Mike told that he had written that letter for 2 hours. (Incorrect - this changes the meaning to a completed action, not a continuous one)

• C. Mike said that he was writing that letter for 2 hours. (Incorrect - this changes the tense to past continuous, losing the "for 2 hours" implication)

• D. Mike told that he had been writing that letter for 2 hours. (Correct - "have been writing" becomes "had been writing")

Therefore, the correct answer for question 2 is D.

3. "Are you going to apply for the scholarship?" Xavier asked.

• This is a direct question starting with "Are," so in indirect speech, we use "whether" or "if."

• The pronoun "you" changes to "I" (from Xavier's perspective of asking) or "he/she" (if reporting to someone else about Xavier's question). The verb "are going" changes to "was going."

• A. Xavier wondered whether you are going to apply for the scholarship. (Incorrect - "are going" should change to the past tense)

• B. Xavier wanted to know whether I was going to apply for the scholarship. (Correct - "you" becomes "I" from the perspective of the person being asked, and "are going" becomes "was going")

• C. Xavier asked whether you were going to apply for the scholarship. (Correct - "you" remains "you" if reporting directly about Xavier's question to the person he asked, and "are going" becomes "were going" to agree with "you")

• D. Xavier asked whether he is going to apply for the scholarship. (Incorrect - "you" should refer to the person being asked)

Both B and C could be correct depending on the context of who is reporting Xavier's question. However, without further context, B is a more common and natural way to report this type of question.

Therefore, the most likely correct answer for question 3 is B.

4. "I did embarrass Daniel in front of the class this afternoon," said Josh.

• The original sentence is in the past simple ("did embarrass").

• When converting to indirect speech, the past simple usually changes to the past perfect ("had embarrassed"). "This afternoon" remains the same as the time reference is still relevant.

• A. Josh admitted having embarrassed Daniel in front of the class that afternoon. (Correct - "did embarrass" becomes "having embarrassed" after "admitted")

• B. Josh admitted embarrassing Daniel in front of the class this afternoon. (Incorrect - the tense is not correctly shifted)

• C. Josh admitted having embarrassed Daniel in front of the class this afternoon. (This is a repetition of A)

• D. Josh admitted that he didn't embarrass Daniel in front of the class that afternoon. (Incorrect - this changes the meaning to a negative statement)

Therefore, the correct answer for question 4 is A (and C, as it's the same).