Construction of arrangements of a cubic and a quartic by patchworking

B. Sturmfels modified Viro's patchworking method and applied it for construction of complete intersections. We use this modification for construction of decomposable curves. We realize 11 new arrangements of an $M$-cubic and an $M$-quartic with 12 common points lying on the odd branch of the cubic and on an oval of the quartic.