[{"_id":"1234","entries":[{"name":"Josh","numbers":[1,2,3,4]}]}]

db.collection.aggregate({$match:{"entries.numbers":{$in:[1,2,3,4]}}},{"$addFields":{"matchingCount":{$size:{$filter:{input:"$entries",as:"e",cond:{$eq:["$$e.numbers",[1,2,3,4]]}}}}}})