An office telephone system cost $32,000.00 with an estimated residual value of $2,000.00. the system has an estimated useful life of 5 years. using the sum-of-the-years’-digits method, the amount of depreciation for the fourth year is $6,000.00. $8,000.00. $4,000.00. $10,000.00.

Sum of the year's digits is 5 + 4 + 3 + 2 +1 = 15 years. 
Depreciation base: 32,000 - 2,000 = 30,000
The depreciation applied in any year is the depreciation base times (number of years remaining divided by 15). The first year has the highest depreciation, and the fifth year has the lowest. 
Depreciation:
1st Year: Dep Base x 5/15
2nd Year: Dep Base x 4/15
3rd Year: Dep Base x 3/15
4th Year: Dep Base x 2/15 = 30,000 x 2/15 = 4,000
5th Year: Dep Base x 1/15

Answer is $4,000