All you need is GROUP BY student and COUNT(DISTINCT):

SELECT student, COUNT(DISTINCT subject) AS "# of subjects" 
FROM students_subjects
GROUP BY student;

You need to group

    CREATE TABLE `student_subject` (
      `name` varchar(256) DEFAULT NULL,
      `subject` varchar(256) DEFAULT NULL
    ) ENGINE=InnoDB DEFAULT CHARSET=latin1;

    --
    -- Dumping data for table `student_subject`
    --

    INSERT INTO `student_subject` (`name`, `subject`) VALUES
    ('James', 'English'),
    ('James', 'Physics'),
    ('Paul', 'Mathematics'),
    ('Paul', 'English'),
    ('Paul', 'English'),
    ('Paul', 'French'),
    ('Jake', 'Mathematics'),
    ('Jake', 'French');

 SELECT name, COUNT(distinct subject) AS "subject_count" 
 FROM student_subject
 GROUP BY name,subject order by name desc

#########output##############

 Name     subject_count
('Jake' , 2),
('James', 2),
('Paul' , 3);

SELECT student, count(*) 
FROM table
GROUP BY student