I assume fyx means differentiation of f with respect to y followed by differentiation with respect to x, and vice versa for fyx.
fxy = d[d(x^3+8xy)/dx]/dy
=> fxy = d(3x^2 + 8y)/dy
=> fxy = 0 + 8
=> fxy = 8
fyx = d[d(x^3+8xy)/dy]/dx
=> fyx = d[0 + 8x]/dx
=> fyx = d[8x]/dx
=> fyx = 8
The required derivatives are fxy = 8 and fyx = 8.
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