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 (
    1078, 886, 884, 679, 1100, 1103, 603, 
    601, 887, 885, 609, 596, 599, 605, 1094, 
    1093, 1075, 892, 922, 880, 908, 909, 
    910, 900, 672, 896, 882, 902, 926, 895, 
    936, 598, 934, 937, 894, 913, 889, 890, 
    888, 932, 933, 675, 911, 914, 924, 920, 
    918
  ) 
GROUP BY 
  p.product_id

Query time 0.00060

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "5.63"
    },
    "grouping_operation": {
      "using_temporary_table": true,
      "using_filesort": true,
      "cost_info": {
        "sort_cost": "0.13"
      },
      "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": "12.95",
            "cost_info": {
              "read_cost": "1.00",
              "eval_cost": "0.03",
              "prefix_cost": "5.34",
              "data_read_per_join": "3"
            },
            "used_columns": [
              "thread_id",
              "object_id",
              "object_type"
            ],
            "attached_condition": "((`cscart`.`cscart_discussion`.`object_id` in (1078,886,884,679,1100,1103,603,601,887,885,609,596,599,605,1094,1093,1075,892,922,880,908,909,910,900,672,896,882,902,926,895,936,598,934,937,894,913,889,890,888,932,933,675,911,914,924,920,918)) 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": "0.13",
              "eval_cost": "0.03",
              "prefix_cost": "5.50",
              "data_read_per_join": "869"
            },
            "used_columns": [
              "product_id"
            ]
          }
        }
      ]
    }
  }
}