Before you use one of the encyclopedias, check (its, their) copyright date
a. its
b. their

The question says,'before you use one of the encyclopedias, check its copyright date'. The correct option is A. This is because, the statement is referring to only one of the encyclopedias, and the correct possessive noun for an inanimate object like encyclopedia is it's. 'Their' will only be correct if the statement is referring to all the encyclopedias.