$3(sin^2x-cos^2x)(sin^6x+sin^4xcos^2x+sin^2xcos^4x+cos^6x)+4(cos^2x-sin^2x)(cos^4x+cos^2xsin^2x+sin^4x)+4sin^4x$

$=-3cos2x(sin^6x+3sin^2xcos^2x+cos^6x-2sin^2xcos^2x)+4coss2x(cos^4x+sin^4x+2sin^2xcos^2x-sin^2xcos^2x)+6sin^4x$

$=-3cos2x[(sin^2x+cos^2x)^3-2sin^2xcos^2x]+4cos2x[(cos^2x+sin^2x)-sin^2xcos^2x]+6sin^4x$

$=-3cos2x(1-2sin^2xcos^2x)+4cos2x(1-sin^2xcos^2x)+6sin^4x$

$=cos2x-2sin^2xcos^2x+6sin^4x$

$=(1-2sin^2x)-2sin^2x(1-sin^2x)+6sin^4x$

$=1-2sin^2x-2sin^2x+2sin^4x+6sin^4x$

$=1-4sin^2x+8sin^4x$