The correct real-world problem that models the equation \(0.08x = 0.06x + 140\) is:
A certain sum yields $140 more in interest when the interest rate is 8% than when it is 6%.
This statement directly reflects the scenario depicted by the equation, where the left side represents the interest earned at an 8% rate and the right side represents the interest earned at a 6% rate, plus an additional $140.