Using remainder theorem if a polynomial` f(x)` is divided by `(x-a)` then the remainder is given by `f(a)` .
`f(x) = x^3-2x+4`
We want to divide `f(x)` by `(x-2)` . That means `a = 2` .
So by remainder theorem;
Remainder `= f(a) = f(2) = 2^3-2xx2+4 = 8`
So the remainder is 8. The correct answer is given in option a)