I can't seem to make any progress on this and I'm not sure where to start. Any help would be greatly appreciated.

Cliff Barnes Petroleum Corporation's pretax accounting income for the year 2004 was $850,000 and included the following items:

Amortization of goodwill $ 60,000
Amortization of patent 57,000
Depreciation on building 80,000
Extraordinary losses 44,000
Extraordinary gains 150,000
Profit-sharing payments to employees 65,000

Ewing Oil Industries is seeking to purchase Cliff Barnes Petroleum Corporation. In attempting to measure Barnes' normal earnings for 2001, Ewing determines that the fair value of the building is triple the book value and that the remaining economic life is double that used by Barnes. The remaining economic life of the patent is half of what it used to be. Ewing would continue the profit-sharing payments to employees; such payments are based on income before depreciation and amortization.

Compute the normal earnings (for purposes of computing goodwill) of Barnes Petroleum Corporation for the year 2004

Amortization of goodwill?
Neither gaap nor ifrs allow it. Unless you're in some random country, I'd really start to question your teacher.

Haha well if you know the method of calculating the normal earnings I'm sure I can figure out what to do with the goodwill. I'm just 100% lost on how to even start the problem at the moment.

German HGB allows amortization of goodwill.