You can use an aggregation pipeline like this:

• First $match to get only documents with desired _id.
• Then $unwind to get different values inside array.
• Match again to get the values which isActive value is Y.
• And $group adding one for each document that exists (i.e. counting documents with isActive= Y). The count is stores in field total.

db.collection.aggregate([
  {
    "$match": {"id": 1}
  },
  {
    "$unwind": "$contact"
  },
  {
    "$match": {"contact.isActive": "Y"}
  },
  {
    "$group": {
      "_id": "$id",
      "total": {"$sum": 1}
    }
  }
])

Example here