。
Do you know my big brother Masao?
Literal
I [of-の] older-brother [of-の] Masao [object-を] know-am [question-かい].
僕の兄の正夫 uses double の: '[my] [brother] Masao' — the second の is appositive, naming-by-attachment ('[my brother] [=] Masao'). 兄 is the humble form for one's own older brother. かい is a casual masculine question particle — softer than か, often used with elder-addressing-younger tone.