CREATE TABLE Parents(id int, name varchar)
CREATE TABLE Items(id int, parent_id int, field_A int,field_B int)

SELECT p.id, p.name, count1, count2 FROM Parents p
INNER JOIN 
(SELECT count(id) as count1, parent_id FROM Items WHERE field_A=1 GROUP BY parent_id) select1 ON select1.parent_id=p.id
INNER JOIN 
(SELECT count(id) as count2, parent_id FROM Items WHERE field_A=1 AND field_B=2 GROUP BY parent_id)
select2 ON select2.parent_id=p.id

insert into items(id,parent_id, field_A, field_B) values(1,1,1,1);
insert into items(id,parent_id, field_A, field_B) values(2,1,1,2);
insert into items(id,parent_id, field_A, field_B) values(3,1,2,1);
insert into items(id,parent_id, field_A, field_B) values(4,1,2,2);
insert into items(id,parent_id, field_A, field_B) values(5,2,1,2);
insert into items(id,parent_id, field_A, field_B) values(6,2,1,3);
insert into items(id,parent_id, field_A, field_B) values(7,1,1,3);
insert into items(id,parent_id, field_A, field_B) values(8,2,1,2);
insert into items(id,parent_id, field_A, field_B) values(9,2,1,2);