Database
[{"code":[{"k":"2016-06-18T18","v":1},{"k":"2016-06-18T21","v":2},{"k":"2016-07-19T00","v":13},{"k":"2015-06-19T03","v":6},{"k":"2015-07-19T06","v":6}]}]
Query
db.collection.aggregate([{$set:{code:{$filter:{input:"$code",cond:{$and:[{$eq:[{$substr:["$$this.k",0,4]},"2016"]},{$eq:[{$substr:["$$this.k",5,2]},"06"]}]}}}}}])