[{_id:"...",firstName:"john",lastName:"Doe",cars:[{"_id":"...","carName":"BMW","carModel":"330","carColor":"silver"},{"_id":"...","carName":"BMW","carModel":"330","carColor":"pink"},{"_id":"...","carName":"Lexus","carModel":"IS300","carColor":"white"},{"_id":"...","carName":"LADA","carModel":"2106","carColor":"blue"}]}]

db.collection.aggregate([{$match:{firstName:"john"}},{$project:{cars:{$filter:{input:"$cars",as:"cars",cond:{$eq:["$$cars.carName","BMW"]}}}}},{$project:{_id:0,"colors":"$cars.carColor"}}])