This is far less complicated to do than the description might seem. It's simple but challenging. My students LOVE the results they're feeling from this.
By extending the legs and adding rotation of the shoulder (twist), these movements target the lower abdominals and obliques (waist).
While lying with back down on the mat, bend knees and do regular crunches (lifting the shoulders while contracting abs, hands behind head for support -- head, neck & shoulders in line with each other).
Then extend right leg straight and place it so it rests on the floor at a 45-degree angle to the right of the body. Continue lifting shoulders straight up.
Now lift left shoulder toward right hip, 8 repetitions.
Next, with right arm extended and placed on floor straight out to the right side (like half a letter T), lift left shoulder toward right hand, 8 repetitions.
Repeat, reducing to 4 reps at each of the two angles; then reduce to 2 reps and finally 1 rep per move, so you are alternating the two types of movements.
Repeat on opposite side of body.