CREATE TABLE `model` (
  `type_id` int(11) NOT NULL,
  `mark_id` int(11) NOT NULL,
  `doc_id` int(11) NOT NULL,
  KEY `mid` (`mark_id`)
) ENGINE=MyISAM DEFAULT CHARSET=utf8 PACK_KEYS=1;

INSERT INTO `model` (`type_id`, `mark_id`, `doc_id`)
VALUES
	(12,3,1426),
	(12,3,1426),
	(12,3,1426),
	(12,3,1427),
	(12,3,1427),
	(12,1,378),
	(12,1,378),
	(12,1,378);

SELECT 
	ml.type_id,
	ml.mark_id,
	ml.doc_id
FROM model AS ml
WHERE 1=1
	AND ml.type_id = 12
GROUP BY ml.doc_id
ORDER BY ml.mark_id,ml.doc_id
;

------------------------------
| type_id | mark_id | doc_id |
------------------------------
| 12      | 1       | 378    |
| 12      | 3       | 1426   |
| 12      | 3       | 1427   |
------------------------------

SELECT 
	ml.type_id,
	ml.mark_id,
	COUNT( SELECT ml2.doc_id FROM model AS ml2 WHERE ml2.type_id=12 AND ml2.mark_id=ml.mark_id GROUP BY ml2.doc_id ) AS docCount,
	ml.doc_id
FROM model AS ml
WHERE 1=1
	AND ml.type_id = 12
GROUP BY ml.doc_id
ORDER BY ml.mark_id,ml.doc_id
;

You have an error in your SQL syntax;
check the manual that corresponds to your MySQL server version for the right syntax to use near 
'SELECT ml2.doc_id FROM model AS ml2 WHERE ml2.type_id=12 AND ml2.mark_id=ml.mark' at line 4

SELECT 
	ml.type_id,
	ml.mark_id,
	( SELECT COUNT(ml2.doc_id) FROM model AS ml2 WHERE ml2.type_id=12 AND ml2.mark_id=ml.mark_id GROUP BY ml2.doc_id ) AS docCount,
	ml.doc_id
FROM model AS ml
WHERE 1=1
	AND ml.type_id = 12
GROUP BY ml.doc_id
ORDER BY ml.mark_id,ml.doc_id
;

Subquery returns more than 1 row

SELECT COUNT(ml2.doc_id) FROM model AS ml2 WHERE ml2.type_id=12 AND ml2.mark_id=3 GROUP BY ml2.doc_id

SELECT 
	ml.type_id,
	ml.mark_id,
	COUNT( SELECT ml2.doc_id FROM model AS ml2 WHERE ml2.type_id=12 AND ml2.mark_id=ml.mark_id GROUP BY ml2.doc_id ) AS docCount,
	ml.doc_id
FROM model AS ml
WHERE 1=1
	AND ml.type_id = 12
GROUP BY ml.doc_id
ORDER BY ml.mark_id,ml.doc_id
;