Oracle の場合、これは次のクエリになります。
SELECT d.Dept_Name
FROM (
SELECT rownum AS position, a.*
FROM (
SELECT Dept_ID, SUM(Emp_Salary) as Total_Salary
FROM employees
GROUP BY Dept_ID
ORDER BY Total_Salary DESC
) a
) b
INNER JOIN department d ON d.Dept_ID = b.Dept_ID
WHERE b.position = 2
ここで動作する Oracle SQLFiddle の例を見ることができます: http://sqlfiddle.com/#!4/f5602/17
完全を期すために、DBMS が MySQL の場合、次のクエリでうまくいきます。
SELECT d.Dept_Name
FROM (
SELECT Dept_ID, SUM(Emp_Salary) as Total_Salary
FROM employees
GROUP BY Dept_ID
ORDER BY Total_Salary DESC
LIMIT 1,1
) a
INNER JOIN department d ON d.Dept_ID = a.Dept_ID
ここで MySQL SQLFiddle の動作例を確認できます: http://sqlfiddle.com/#!2/738e0/15