Since your function key is an array, in order to use the $match operator, first you have to use the $unwind operator. http://docs.mongodb.org/manual/reference/aggregation/unwind/
And then you use $match operator to find the documents that you want http://docs.mongodb.org/manual/reference/aggregation/match/
So your query should look like this
db.collection.aggregate([{$unwind:"$Function"},{$match:{"Form_id":1,"Function.Function_id":2}}])
By default mongo will display the _id of the document. So if you do not want to display the _id, after matching the relevant ones, you could use the $project operator http://docs.mongodb.org/manual/reference/aggregation/project/
db.collection.aggregate([{$unwind:"$Function"},{$match:{"Form_id":1,"Function.Function_id":2}},{$project:{"_id":0,"Form_id":1,"Function":1}}])
If you don't want the form_id to be displayed, simply don't specify the form_id in the project part of the query. By default mongo will only display the keys whose value is 1. If the key is not mentioned it will not display it.
db.collection.aggregate([{$unwind:"$Function"},{$match:{"Form_id":1,"Function.Function_id":2}},{$project:{"_id":0,"Function":1}}])