Your opponent doesnt have a graveyard so they do not return a creature. You have 2 graveyards, so you can pick which one you will return a creature from. You still only get to return 1 creature total
W may only be paid with white mana. U may only be paid with blue mana. B may only be paid with black mana. R may only be paid with red mana. G may only be paid with green mana. C may only be paid with colorless mana. 1 may be paid with white, blue, black, red, green, or clolorless mana.
I would say that the word *also* implies that opponent graveyards belong to both your opponent, and you, so two creatures would return. This is un-land though, so unless there is a ruling, the answer is probably "whatever you argue best".
**EDIT** The Unstable FAQ says that the graveyards belong to no one else, under Graveyard Busybody. Looks like peteroupc and myself were wrong; you would only get one creature.
With the understanding that no Magic card (other than "silver-bordered" cards) has such an effect as that of either of Graveyard Busybody's abilities:
The word "also" in Graveyard Busybody's first ability suggests that each graveyard is treated as "your graveyar[d]" in addition to being treated as its owner's. Thus, every other player still has a graveyard despite that ability. In the case of Exhume, though, there is a difficulty if you and another player want to return the same creature card to the battlefield; in which case C.R. 101.4 (the APNAP order rule) can be applied.
EDIT: See also comment 3 and the second note below this one. Note, however, that because no Magic card (other than "silver-bordered" cards) has such an effect as that of Graveyard Busybody's first ability, the comprehensive rules do not regulate, and therefore cannot answer, whether a graveyard that is "also" a particular player's graveyard is still the graveyard of its original owner.
EDIT (Jan. 16): Correctness edit in view of changes to the Magic Tournament Rules with Rivals of Ixalan.
EDIT (Jan. 2, 2019): Note that the comprehensive rules do not regulate, and therefore cannot answer, whether a graveyard that is "also" a particular player's graveyard is still the graveyard of its original owner. In general, in a game allowing "silver-bordered" cards such as those in Unglued, Unhinged, and Unstable, the players in the game can agree on modifications to the comprehensive rules ("house rules") to accommodate situations, such as this one, that the comprehensive rules neither regulate nor answer and that are unique to such cards (see also C.R. 100.7). Although Mark Rosewater issues "rulings" on how certain game situations unique to such cards play out, such advice is no more or less valid than the "house rules" agreed to by the players (that is, such players can agree whether to adopt such "rulings" or not).
[180 classic cube]
**EDIT** The Unstable FAQ says that the graveyards belong to no one else, under Graveyard Busybody. Looks like peteroupc and myself were wrong; you would only get one creature.
The word "also" in Graveyard Busybody's first ability suggests that each graveyard is treated as "your graveyar[d]" in addition to being treated as its owner's. Thus, every other player still has a graveyard despite that ability. In the case of Exhume, though, there is a difficulty if you and another player want to return the same creature card to the battlefield; in which case C.R. 101.4 (the APNAP order rule) can be applied.EDIT:
See also comment 3 and the second note below this one. Note, however, that because no Magic card (other than "silver-bordered" cards) has such an effect as that of Graveyard Busybody's first ability, the comprehensive rules do not regulate, and therefore cannot answer, whether a graveyard that is "also" a particular player's graveyard is still the graveyard of its original owner.EDIT (Jan. 16): Correctness edit in view of changes to the Magic Tournament Rules with Rivals of Ixalan.
EDIT (Jan. 2, 2019): Note that the comprehensive rules do not regulate, and therefore cannot answer, whether a graveyard that is "also" a particular player's graveyard is still the graveyard of its original owner. In general, in a game allowing "silver-bordered" cards such as those in Unglued, Unhinged, and Unstable, the players in the game can agree on modifications to the comprehensive rules ("house rules") to accommodate situations, such as this one, that the comprehensive rules neither regulate nor answer and that are unique to such cards (see also C.R. 100.7). Although Mark Rosewater issues "rulings" on how certain game situations unique to such cards play out, such advice is no more or less valid than the "house rules" agreed to by the players (that is, such players can agree whether to adopt such "rulings" or not).
EDIT (Jan. 26, 2019): Struck out more text.