Database

[{"_id":ObjectId("60a2c0621e5f043b735e36ef"),"car_id":78,"terminal":"JFK","gists":["A","M","C","D","Q","J","F"]},{"_id":ObjectId("60a2c0621e5f043b735e36f0"),"car_id":79,"terminal":"LAX","gists":["A","M","C","D","Q","J","F","A"]},{"_id":ObjectId("60a2c0621e5f043b735e36f1"),"car_id":80,"terminal":"ORD","gists":["A","M","N","L","Q","A","O"]},{"_id":ObjectId("60a2c0621e5f043b735e36f2"),"car_id":81,"terminal":"MIA","gists":["X","L","X","D","Q","E","E"]},{"_id":ObjectId("60a2c0621e5f043b735e36f3"),"car_id":82,"terminal":"ORD","gists":["H","H","C","D","A","B","C"]},{"_id":ObjectId("60a2c0621e5f043b735e36f4"),"car_id":83,"terminal":"JFK","gists":["X","Q","K","D","C","J","F"]},]

Query

db.collection.aggregate([{"$project":{"gists":1}},{"$unwind":"$gists"},{"$group":{"_id":{"_id":"$_id","cid":"$gists"},"count":{"$sum":1}}},{"$match":{"$and":[{"count":{"$gt":1}},{"gists":"A"}]}},{"$group":{"_id":"$_id._id","gists":{"$addToSet":"$_id.cid"}}}])

Result