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 (
    4970, 4963, 4974, 4978, 4956, 4962, 4959, 
    12457, 11777, 12268, 12270, 12271, 
    12272, 12275, 12276, 12255, 12257, 
    12258, 12259, 12260, 12261, 12262, 
    12269, 12263, 12264, 12265, 12266, 
    12267, 12273, 12274
  ) 
GROUP BY 
  p.product_id

Query time 0.00055

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 (4970,4963,4974,4978,4956,4962,4959,12457,11777,12268,12270,12271,12272,12275,12276,12255,12257,12258,12259,12260,12261,12262,12269,12263,12264,12265,12266,12267,12273,12274)",
          "using_index": true
        }
      }
    }
  }
}