SELECT 
  p.product_id, 
  ifnull(
    count(dp.post_id), 
    0
  ) as discussion_amount_posts 
FROM 
  q_discussion 
  INNER JOIN q_products as p ON (
    q_discussion.object_id = p.product_id
  ) 
  INNER JOIN q_discussion_posts as dp ON (
    q_discussion.thread_id = dp.thread_id 
    AND q_discussion.object_type = 'P'
  ) 
WHERE 
  dp.status = 'A' 
  and p.product_id in (
    3628, 3629, 3630, 3631, 3632, 3633, 3634, 
    3635, 3636, 3637, 3638, 3639, 3640, 
    3641, 3642, 3643, 3644, 3645, 3646, 
    3647, 3648, 3649, 3650, 3651, 3652, 
    3653, 3654, 3655, 3656, 3657, 3658, 
    3659
  ) 
GROUP BY 
  p.product_id

Query time 0.00071

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "21.61"
    },
    "grouping_operation": {
      "using_temporary_table": true,
      "using_filesort": true,
      "cost_info": {
        "sort_cost": "0.29"
      },
      "nested_loop": [
        {
          "table": {
            "table_name": "dp",
            "access_type": "ALL",
            "possible_keys": [
              "thread_id",
              "thread_id_2"
            ],
            "rows_examined_per_scan": 57,
            "rows_produced_per_join": 5,
            "filtered": "10.00",
            "cost_info": {
              "read_cost": "13.01",
              "eval_cost": "1.14",
              "prefix_cost": "14.15",
              "data_read_per_join": "2K"
            },
            "used_columns": [
              "post_id",
              "thread_id",
              "status"
            ],
            "attached_condition": "(`portal`.`dp`.`status` = 'A')"
          }
        },
        {
          "table": {
            "table_name": "q_discussion",
            "access_type": "eq_ref",
            "possible_keys": [
              "PRIMARY",
              "object_id"
            ],
            "key": "PRIMARY",
            "used_key_parts": [
              "thread_id"
            ],
            "key_length": "3",
            "ref": [
              "portal.dp.thread_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 0,
            "filtered": "5.00",
            "cost_info": {
              "read_cost": "5.70",
              "eval_cost": "0.06",
              "prefix_cost": "20.99",
              "data_read_per_join": "4"
            },
            "used_columns": [
              "thread_id",
              "object_id",
              "object_type"
            ],
            "attached_condition": "((`portal`.`q_discussion`.`object_id` in (3628,3629,3630,3631,3632,3633,3634,3635,3636,3637,3638,3639,3640,3641,3642,3643,3644,3645,3646,3647,3648,3649,3650,3651,3652,3653,3654,3655,3656,3657,3658,3659)) and (`portal`.`q_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": [
              "portal.q_discussion.object_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 0,
            "filtered": "100.00",
            "using_index": true,
            "cost_info": {
              "read_cost": "0.29",
              "eval_cost": "0.06",
              "prefix_cost": "21.33",
              "data_read_per_join": "1K"
            },
            "used_columns": [
              "product_id"
            ]
          }
        }
      ]
    }
  }
}