Amount borrowed = 750

Future Value of 750 (6% 6 months; 8% 12 months) = Future Value of 18 payments (similar interest)

Formula for FV of amount A: FV = A(1 + i)^n

Formula for FV of payment P: FV = P[(1 + i)^n - 1] / i

Let x = .06/12 and y = .08/12

FV of 750: [750(1 + x)^6](1 + y)^12

FV of P: {P[(1 + x)^6 - 1](1 + y)^12} / x + {P[(1 + y)^12 - 1]} / y

{P[(1 + x)^6 - 1](1 + y)^12} / x + {P[(1 + y)^12 - 1]} / y = [750(1 + x)^6](1 + y)^12

Py[(1 + x)^6 - 1](1 + y)^12 + Px[(1 + y)^12 - 1] = [750xy(1 + x)^6](1 + y)^12

P = {[750xy(1 + x)^6](1 + y)^12} / {y[(1 + x)^6 - 1](1 + y)^12 + x[(1 + y)^12 - 1]}

Substitute x = .06/12 and y = .08/12 back in to get P = 43.97989... or 43.98 rounded.

If you're confused with this: P[(1 + x)^6 - 1](1 + y)^12

it means the accumulation of 6 payments at 6% earns 8% during next 12 months.