Final answer:
The most possible slip systems in fcc metals are twelve, corresponding to the combination of the four {111} planes and the three <110> directions within each plane.
Step-by-step explanation:
The student's question pertains to the most possible slip systems in fcc metals (face-centered cubic metals). In metals with an FCC crystal structure, slip typically occurs along the densest packed directions and planes. In the FCC structure, there are four atoms per unit cell, with atoms located at the corners and centers of each face of the cube. The close-packed planes are the {111} planes, and the close-packed directions are the <110> directions. Because there are four {111} planes and three <110> directions possible for each plane, there is a total of 12 slip systems in an FCC crystal.