The engagement is the distance that separates the point where the posterior is going to take place, from the vertical of the lumbosacral articulation. What makes the depth of the engagement is the articular angles that contribute to the increase of the distance. The hip tilt is the determining factor. Two cases occur: either the posterior limb is in extension, or all the joints are flexed.
One of the exercises that I find is the most for the commitment is: the neck descents correctly performed in a sufficient pulse will relax the top line and promote the thrust of the hindquarters and therefore their commitment. The most difficult when exercising on the engagement is not to lose touch and especially not to deteriorate the pace.
The extension is an amplification of a pace, by balanced and elastic extension of the gestures, allowing an increase in the initial amplitude, specific to each horse. The longitudinal relaxations must allow the horse to increase his stride to the maximum until he is misjudged.
Before asking for an elongation, the horse must be in a dynamic work have a good attitude and especially have a good cadence. One exercise I like to do is the shoulder within.
By working from one shoulder to the inside, one seeks to extend the stride and starting on a large circle at the end of the shoulder within one has an elongation almost natural. If the internal shoulder is well executed, the horses are obliged to stand on the circle, so that they are less easily removed from the attitude and the cadence, and in this case the elongation can be demanded, There is precipitation. Simpler and in the same logic, you have the work on the circle and once you feel that your horse is ready you leave on a diagonal.
Have a good day !!