A) The green curve is the easy one; it's the (110) direction because there's no degeneracy. The blue is the (111) and the red, the (100). Either remember that the transverse (111) modes have the lowest velocity of sound, or else note that the maximum in the blue curve occurs at a lower q-value than the maximum of the red one. (See part B for more.)
B) The L point, on the (111) face of the BZ, is at a distance (pi/a)sqrt(3) from the origin, and the X point, on the (100) face, is at a distance (2 pi/a). They are both at maxima of the dispersion curves, hence the X is at the top of the red curve, the L at the maximum of the blue. (This was one of the rationales for the color choice in part A.) The K point is the mess to work out and turns out to be a distance (3 pi/a)/sqrt(2) from the origin, hence further out than the X point, but not as far as the end of the graph.