。
Who do you think she's living with?
Literal
She [topic-は] who [with-と] together is-living [quotative-と] [you-think-思いますか]?
An embedded-question construction: the inner clause 彼女は誰といっしょに暮らしている (a question about 'whom') is fed to 思う ('think') via the quotative と and turned into a polite question with 思いますか. English flips the question word forward in such constructions ('Who do you think she's living with?'); Japanese keeps it in its base position. と here is also the comitative 'with,' marking 誰 ('who') as the co-resident.