∵m,n是方程X²-3X+1=0的两根,
∴m+m=3,mn=1,
2m²+4n²-6n+1996
=2m^2+2n^2+2n^2-6n+1996
=2(m^2+n^2)+2(n^2-3n)+1996
=2[(m+n)^2-2mn]+2*(-1)+1996
=2(3^2-2)-2+1996
=2*7+1994
=14+1994
=2018