Double under-hooks is the key to turning the half guard position into an offensive position. The ability to control your opponent becomes available once you have the double under-hooks and the Lockdown in place properly. The proximity to sweeping your opponent and getting to a top position is now just a step away.
However, achieving double under-hooks can be quite the battle in and of itself. Often, you opponent on top will be doing everything they can to secure one under-hook they need in order to pass your guard. If your opponent tries passing without an under-hook, you can simply take their back. The goal is to win the under-hook battle while using the legs to Lockdown and distract your opponent in order to help achieve this goal.
Start pummeling immediately. Get your left arm under your opponents right arm on the same side that the Lockdown is on.
Use your right forearm and control your opponents left arm passed their elbow. While doing this, reach through with your left arm.
Grab you hands together and while continuing to stretch out the Lockdown.
Grip your hands together using a Gable Grip. Wrap your fingers around the outside of your thumbs.