Horizontal Muay Thai Elbow Body Alignments:
The striking arm is parallel to the ground in line with the shoulder. The palm of the striking arm faces the ground. The defending arm is bent at a 90 degree angle and the inside of the wrist the braced against the forehead (or the palm is braced on the side of the forehead, both are valid) to protect against counter elbows. 
The hips and torso have turned sharply into the movement. The foot of you striking side has pivot freely into the movement, turning the heel out.
Horizontal Muay Thai Elbow Movement:
From your kick stance when your deliver your horizontal Muay Thai elbow the non-striking hand pulls into the forehead to defend. The striking arm rotates till the palm faces the ground and the elbow is at shoulder height out from your side. All the power of this technique comes from your core. Shift your weight to the non-striking side as you sharply turn the hip and torso toward the opponent. Allow the non-weighted foot to pivot freely with the movement. When you deliver the Horizontal Muay Thai Elbow, strike with the last two inches of the forearm and put all of your weight and core strength into the blow. Reverse these movements to recoil back into your Muay Thai Kick Stance
Horizontal Muay Thai Elbow Combinations:
Parry – Single Arm Shield and Catch – V-cover – L-Horizontal Muay Thai Elbow – Right Straight Punch – L Uppercut – R-Horizontal Muay Thai Elbow. From the clinch: R-Cup Knee – L-Straight Knee – Pop out and R-Horizontal Muay Thai Elbow