Please help on this Italian sentence

anyone?

For me it's correct. I would say it in a main clause.

It's one of the multiple ways you can say so.
(your book, they would appreciate it a lot).

Hi.

The sentence is quite correct, but I would remove "loro" because it is not necessary and sound redundant. The verb is not conjunctive, it is conditional (condizionale in Italian) and can be the main verb. It is used to express a condition or a doubt, often with a secondary sentence with the conjunctive. I'll make some example:

Il tuo libro, lo apprezzerebbero molto se solo potessero leggerlo
That's a condition: If they could read your book they would appreciate it a lot.

Questo sarebbe tuo fratello?
That's a doubt: could this be your brother?

And so on... Remember anyway that the conditional never express a statement: if you say: "Il tuo libro, lo apprezzerebbero molto" You mean that they would appreciate the book, but there is some reason, whatever it is, because you think they can not. If you want to say they will actually appreciate the book you should use the indicative: "Il tuo libro, lo apprezzeranno molto"

Hope this will be useful.