Here is answer for your question.
db.getCollection('users').aggregate([
{$match : {admin : 1}},
{$lookup: {from: "posts",localField: "_id",foreignField: "owner_id",as: "posts"}},
{$project : {
posts : { $filter : {input : "$posts" , as : "post", cond : { $eq : ['$$post.via' , 'facebook'] } } },
admin : 1
}}
])
Or either you can go with mongodb group option.
db.getCollection('users').aggregate([
{$match : {admin : 1}},
{$lookup: {from: "posts",localField: "_id",foreignField: "owner_id",as: "posts"}},
{$unwind : "$posts"},
{$match : {"posts.via":"facebook"}},
{ $group : {
_id : "$_id",
posts : {$push : "$posts"}
}}
])