You can't delete the record as there is no uniqueness in your records.
So can select the records without duplicating the records.
Refer below query.
SQL
CREATE TABLE #Class1
( 
	name VARCHAR(50),
	class VARCHAR(50)
)
INSERT INTO #Class1(name, class) VALUES ('A', 'First')
INSERT INTO #Class1(name, class) VALUES ('A', 'Second')
INSERT INTO #Class1(name, class) VALUES ('B', 'First')
INSERT INTO #Class1(name, class) VALUES ('A', 'Third')
INSERT INTO #Class1(name, class) VALUES ('B', 'First')
INSERT INTO #Class1(name, class) VALUES ('A', 'First')
SELECT name, class 
FROM
(
	SELECT ROW_NUMBER() OVER (PARTITION BY name,class ORDER BY (select 0)) Number,
	name, class
	FROM #Class1
)p
WHERE Number = 1
OR 
SELECT DISTINCT name, class from #class1
Output
 
| name | class | 
| A | First | 
| A | Second | 
| A | Third | 
| B | First |