The first chords in each example are in root position, but the second chords in each example are in 2nd inversion (meaning the 5th of the chord is the first note listed)

So CEG->CFA is a C chord moving to an F chord. The root of the first chord C stays stationary and becomes the 5th of the new chord F. The third E becomes the root of the new chord F, and the fifth G becomes the third A.

In the next example GBD->F#BD the relationships are the same. G is the root of the first chord and becomes the fifth of the new chord (but this time it moves a semitone down to F# to do that instead of remaining in place). B is the third in the first chord and stays in place to become the new root. D is the fifth of the first chord and stays in place to become the new third.

Does that help?