SELECT 
  p.product_id, 
  ifnull(
    count(dp.post_id), 
    0
  ) as discussion_amount_posts 
FROM 
  cscart_discussion 
  INNER JOIN cscart_products as p ON (
    cscart_discussion.object_id = p.product_id
  ) 
  INNER JOIN cscart_discussion_posts as dp ON (
    cscart_discussion.thread_id = dp.thread_id 
    AND cscart_discussion.object_type = 'P'
  ) 
WHERE 
  dp.status = 'A' 
  and p.product_id in (
    801, 800, 799, 798, 797, 806, 805, 804, 
    803, 802, 810, 809, 808, 807, 812, 811, 
    814, 813, 818, 817, 816, 815, 823, 822
  ) 
GROUP BY 
  p.product_id

Query time 0.00060

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "5.49"
    },
    "grouping_operation": {
      "using_temporary_table": true,
      "using_filesort": true,
      "cost_info": {
        "sort_cost": "0.07"
      },
      "nested_loop": [
        {
          "table": {
            "table_name": "dp",
            "access_type": "ALL",
            "possible_keys": [
              "thread_id",
              "thread_id_2"
            ],
            "rows_examined_per_scan": 10,
            "rows_produced_per_join": 1,
            "filtered": "10.00",
            "cost_info": {
              "read_cost": "3.94",
              "eval_cost": "0.20",
              "prefix_cost": "4.14",
              "data_read_per_join": "448"
            },
            "used_columns": [
              "post_id",
              "thread_id",
              "status"
            ],
            "attached_condition": "(`cscart`.`dp`.`status` = 'A')"
          }
        },
        {
          "table": {
            "table_name": "cscart_discussion",
            "access_type": "eq_ref",
            "possible_keys": [
              "PRIMARY",
              "object_id"
            ],
            "key": "PRIMARY",
            "used_key_parts": [
              "thread_id"
            ],
            "key_length": "3",
            "ref": [
              "cscart.dp.thread_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 0,
            "filtered": "6.61",
            "cost_info": {
              "read_cost": "1.00",
              "eval_cost": "0.01",
              "prefix_cost": "5.34",
              "data_read_per_join": "1"
            },
            "used_columns": [
              "thread_id",
              "object_id",
              "object_type"
            ],
            "attached_condition": "((`cscart`.`cscart_discussion`.`object_id` in (801,800,799,798,797,806,805,804,803,802,810,809,808,807,812,811,814,813,818,817,816,815,823,822)) and (`cscart`.`cscart_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": [
              "cscart.cscart_discussion.object_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 0,
            "filtered": "100.00",
            "using_index": true,
            "cost_info": {
              "read_cost": "0.07",
              "eval_cost": "0.01",
              "prefix_cost": "5.42",
              "data_read_per_join": "443"
            },
            "used_columns": [
              "product_id"
            ]
          }
        }
      ]
    }
  }
}