use the sum of angles's trigonometric identity formula:
cos(A+B)=(cosAcosB-sinAsinB)
x+y=4cos(t+π/6)+2sint=4(cost*cosπ/6-sint*sinπ/6)+2sint
recall that cosπ//6=√3/2, and sinπ/6=1/2:
4(cost*cosπ/6-sint*sinπ/6)+2sint=4[(√3/2)cost-(1/2)sint]+2sint
simplify:2√3cost-2sint+2sint=2√3cost