solve triangle XYZ where angle X=40, x=12 and y=6

Law of Sines: sinY=(6/12)sin40
sinY=0.3214
Y=arcsine(0.3214)
Y=18.747

Since all angles must add to 180 degrees:
Z=180-40-18.747=121.25
now we find z...
z=12(sin121.25/sin40)=15.96