[{"test":"other","list":[{"number":[{"value":"1"},{"value":"2"},{"value":"2"}]},{"number":[{"value":"1"},{"value":"2"},{"value":"2"}]},{"number":[{"value":"1"},{"value":"2"}]}]}]

db.collection.aggregate([{$project:{test:"$test",count:{$reduce:{input:"$list",initialValue:0,in:{$add:["$$value",{$size:"$$this.number"}]}}}}}])