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 (
    4070, 4154, 4144, 4152, 4153, 4029, 4026, 
    3999, 4003, 4005, 4155, 4156, 4157, 
    4158, 4159, 4160, 4114, 4112, 4204, 
    4208, 4209, 4210, 4110, 4111, 4130, 
    4132, 4133, 4134, 3977, 4055
  ) 
GROUP BY 
  p.product_id

Query time 0.00033

JSON explain

{
  "query_block": {
    "select_id": 1,
    "filesort": {
      "sort_key": "p.product_id",
      "temporary_table": {
        "table": {
          "table_name": "dp",
          "access_type": "ALL",
          "possible_keys": ["thread_id", "thread_id_2"],
          "rows": 8,
          "filtered": 100,
          "attached_condition": "dp.`status` = 'A'"
        },
        "table": {
          "table_name": "cscart_discussion",
          "access_type": "eq_ref",
          "possible_keys": ["PRIMARY", "object_id"],
          "key": "PRIMARY",
          "key_length": "3",
          "used_key_parts": ["thread_id"],
          "ref": ["ymonline_livedata.dp.thread_id"],
          "rows": 1,
          "filtered": 100,
          "attached_condition": "cscart_discussion.object_type = 'P'"
        },
        "table": {
          "table_name": "p",
          "access_type": "eq_ref",
          "possible_keys": ["PRIMARY"],
          "key": "PRIMARY",
          "key_length": "3",
          "used_key_parts": ["product_id"],
          "ref": ["ymonline_livedata.cscart_discussion.object_id"],
          "rows": 1,
          "filtered": 100,
          "attached_condition": "p.product_id in (4070,4154,4144,4152,4153,4029,4026,3999,4003,4005,4155,4156,4157,4158,4159,4160,4114,4112,4204,4208,4209,4210,4110,4111,4130,4132,4133,4134,3977,4055)",
          "using_index": true
        }
      }
    }
  }
}