Database

[{_id:1,user_id:10,line_items:[{_id:2,quantity:2,},{_id:3,quantity:1,}],purchase_date:ISODate("2021-02-05T21:00:00.000+00:00")}]

Query

db.collection.aggregate([{$group:{_id:{"$month":"$purchase_date"},total:{$sum:{$sum:"$line_items.quantity"}}}}])

Result