The sum of the magnitudes of the coefficients in the expansion of ${\left(1-x+x^2-x^3\right)}^n$, is

The sum of the magnitudes of the coefficients is obtained by replacing $x$by $-1$ in ${(1-x+x^2-x^3)}^n.$

Hence, required sum $={(1+1+1+1)}^n=4^n.$