The trick (which is certainly not obvious) is to ask whether vibrations in two directions will be equivalent to each other. For a diamond crystal (which is fcc witha basis), the crystal is essential identical to the crystal rotated by 90 degrees around the  axis. (Strictly it is equivalent to the rotation plus a translation). As a result a transverse vibration mode where the atoms move in the  direction and the wave moves in the  direction is exactly equivalent to a transverse mode where atoms move in the  direction and the wave moves in the  direction. This means the for both the acoustic and the optical branches, the two transverse modes will have the same frequency.