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 (
    3934, 3935, 3936, 3937, 3955, 3956, 3957, 
    3970, 3971, 3972, 3973, 4010, 4011, 
    4052, 4053, 4065, 4066, 4089, 4090, 
    4091, 4093, 4094, 4095, 4096, 4097, 
    4098, 4099, 4100, 4195, 4196, 4197, 
    4198, 4202, 4203, 4367
  ) 
GROUP BY 
  p.product_id

Query time 0.00030

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 (3934,3935,3936,3937,3955,3956,3957,3970,3971,3972,3973,4010,4011,4052,4053,4065,4066,4089,4090,4091,4093,4094,4095,4096,4097,4098,4099,4100,4195,4196,4197,4198,4202,4203,4367)",
          "using_index": true
        }
      }
    }
  }
}