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 (
    16353, 16352, 16825, 16882, 16850, 16880, 
    16829, 16924, 16774, 15769, 15496, 
    15497, 15768, 15770, 15846, 15795, 
    16791, 16885, 16884, 16854, 16855, 
    16856, 16857, 16851, 16156, 16802, 
    15464, 15466, 15468, 16143, 16141, 
    15465, 16582, 16142, 15467, 15914, 
    16891, 16860, 16379, 16351, 16378, 
    16380, 16381, 16382, 16384, 16383, 
    16385, 16386, 16387, 16388, 16811, 
    16828, 13936, 16783, 15501, 15791, 
    15829, 16794, 16942, 16949, 16950, 
    16810, 16181, 16180, 15790, 16179, 
    16804, 16805, 16922, 16956, 15793, 
    15915, 16793, 15783, 16650, 16395, 
    16394, 16796, 16356
  ) 
GROUP BY 
  p.product_id

Query time 0.00062

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "1.69"
    },
    "grouping_operation": {
      "using_temporary_table": true,
      "using_filesort": false,
      "nested_loop": [
        {
          "table": {
            "table_name": "dp",
            "access_type": "ALL",
            "possible_keys": [
              "thread_id",
              "thread_id_2"
            ],
            "rows_examined_per_scan": 8,
            "rows_produced_per_join": 1,
            "filtered": "12.50",
            "cost_info": {
              "read_cost": "1.22",
              "eval_cost": "0.10",
              "prefix_cost": "1.32",
              "data_read_per_join": "448"
            },
            "used_columns": [
              "post_id",
              "thread_id",
              "status"
            ],
            "attached_condition": "(`dev_yourmart_co_bw`.`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": [
              "dev_yourmart_co_bw.dp.thread_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 0,
            "filtered": "5.00",
            "cost_info": {
              "read_cost": "0.25",
              "eval_cost": "0.01",
              "prefix_cost": "1.67",
              "data_read_per_join": "1"
            },
            "used_columns": [
              "thread_id",
              "object_id",
              "object_type"
            ],
            "attached_condition": "((`dev_yourmart_co_bw`.`cscart_discussion`.`object_id` in (16353,16352,16825,16882,16850,16880,16829,16924,16774,15769,15496,15497,15768,15770,15846,15795,16791,16885,16884,16854,16855,16856,16857,16851,16156,16802,15464,15466,15468,16143,16141,15465,16582,16142,15467,15914,16891,16860,16379,16351,16378,16380,16381,16382,16384,16383,16385,16386,16387,16388,16811,16828,13936,16783,15501,15791,15829,16794,16942,16949,16950,16810,16181,16180,15790,16179,16804,16805,16922,16956,15793,15915,16793,15783,16650,16395,16394,16796,16356)) and (`dev_yourmart_co_bw`.`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": [
              "dev_yourmart_co_bw.cscart_discussion.object_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 0,
            "filtered": "100.00",
            "using_index": true,
            "cost_info": {
              "read_cost": "0.01",
              "eval_cost": "0.01",
              "prefix_cost": "1.69",
              "data_read_per_join": "266"
            },
            "used_columns": [
              "product_id"
            ]
          }
        }
      ]
    }
  }
}