、。
Could you take care of my pets while I'm away?
Literal
Absence [possessive-の] during, pets [possessive-の] care [object-を] do [receive-ていただけますか]?
ペット is a loanword from English. ~ていただけますか is the keigo polite request form — literally 'could I humbly receive your doing X?' — combining the humble auxiliary いただく with its potential and a polite question. Standard for asking a real favor.