SELECT 
  p.product_id, 
  ifnull(
    count(dp.post_id), 
    0
  ) as discussion_amount_posts 
FROM 
  q_discussion 
  INNER JOIN q_products as p ON (
    q_discussion.object_id = p.product_id
  ) 
  INNER JOIN q_discussion_posts as dp ON (
    q_discussion.thread_id = dp.thread_id 
    AND q_discussion.object_type = 'P'
  ) 
WHERE 
  dp.status = 'A' 
  and p.product_id in (
    16250, 16253, 16257, 16259, 16260, 16263, 
    16266, 16267, 16268, 16269, 16270, 
    16271, 16274, 16275, 16295, 16296, 
    16299, 16300, 16302, 16303, 16304, 
    16305, 16306, 16310, 16311, 16312, 
    16313, 16314, 16315, 16316
  ) 
GROUP BY 
  p.product_id

Query time 0.00063

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "21.61"
    },
    "grouping_operation": {
      "using_temporary_table": true,
      "using_filesort": true,
      "cost_info": {
        "sort_cost": "0.29"
      },
      "nested_loop": [
        {
          "table": {
            "table_name": "dp",
            "access_type": "ALL",
            "possible_keys": [
              "thread_id",
              "thread_id_2"
            ],
            "rows_examined_per_scan": 57,
            "rows_produced_per_join": 5,
            "filtered": "10.00",
            "cost_info": {
              "read_cost": "13.01",
              "eval_cost": "1.14",
              "prefix_cost": "14.15",
              "data_read_per_join": "2K"
            },
            "used_columns": [
              "post_id",
              "thread_id",
              "status"
            ],
            "attached_condition": "(`portal`.`dp`.`status` = 'A')"
          }
        },
        {
          "table": {
            "table_name": "q_discussion",
            "access_type": "eq_ref",
            "possible_keys": [
              "PRIMARY",
              "object_id"
            ],
            "key": "PRIMARY",
            "used_key_parts": [
              "thread_id"
            ],
            "key_length": "3",
            "ref": [
              "portal.dp.thread_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 0,
            "filtered": "5.00",
            "cost_info": {
              "read_cost": "5.70",
              "eval_cost": "0.06",
              "prefix_cost": "20.99",
              "data_read_per_join": "4"
            },
            "used_columns": [
              "thread_id",
              "object_id",
              "object_type"
            ],
            "attached_condition": "((`portal`.`q_discussion`.`object_id` in (16250,16253,16257,16259,16260,16263,16266,16267,16268,16269,16270,16271,16274,16275,16295,16296,16299,16300,16302,16303,16304,16305,16306,16310,16311,16312,16313,16314,16315,16316)) and (`portal`.`q_discussion`.`object_type` = 'P'))"
          }
        },
        {
          "table": {
            "table_name": "p",
            "access_type": "eq_ref",
            "possible_keys": [
              "PRIMARY"
            ],
            "key": "PRIMARY",
            "used_key_parts": [
              "product_id"
            ],
            "key_length": "3",
            "ref": [
              "portal.q_discussion.object_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 0,
            "filtered": "100.00",
            "using_index": true,
            "cost_info": {
              "read_cost": "0.29",
              "eval_cost": "0.06",
              "prefix_cost": "21.33",
              "data_read_per_join": "1K"
            },
            "used_columns": [
              "product_id"
            ]
          }
        }
      ]
    }
  }
}