Learn English – Change in narration/speech

Tom shows me two bullets. Tom says, "I found these embedded in the paneling."

Tom has just shown you two bullets. So you now know what two bullets he is talking about it - what the "these" are. So the demonstrative pronoun isn't really needed (but not wrong if you still use it) because what the "these" are is now part of the context.

He said that he found them embedded in the paneling.

This would make a bit more sense if the preceding sentence was something like:

Tom showed me two bullets.

although

Tom showed me two bullets. He said that he found those embedded in the paneling.

is not wrong, but can suggest:

• that you are nowhere near the bullets and are recounting an event that happened some time ago, instead of something that had just happened.

• that you were previously aware that Tom had found "something" but didn't know what it was.

I think the book answer is right. We really can't use "must" to mean "have to" in the past. So we switch to "have to." Then, since it's reported speech, we have to use the conditional "would have to."

I wish books didn't teach "must" in this context, by the way, because it's much rarer than "have to." Nobody would ever say "if the flood gets worse we must leave the house." We'd say "if the flood gets worse, we have to leave the house."