Here is the key: when we remove the strum, the initial tendency for the guitarist will be to stop the strumming motion in the picking hand. This is exactly what we DON'T want to do, because it mixes up the nice pattern we had going of all the downstrums being ON the beat, and all the upstrums being OFF the beat (on the "and" or on the "offbeat".)The trick is to keep the strumming motion going in the picking hand; but ever so slightly lift the hand away from the body of the guitar momentarily, on the downstroke of the 3rd beat, so the pick misses the strings. Then, on the next upstroke (the "and" of the 3rd beat), bring the hand back closer to the body of the guitar, so the pick hits the strings. So, to summarize, the upward/downward motion of the picking hand should not change AT ALL from the first pattern. Deliberately avoiding the strings with the pick on the 3rd beat of the pattern is the only factor that has changed.
Listen to, and play along with, this second strumming pattern, to get a better idea on how this new pattern should sound. Once you are comfortable with this, try it at a somewhat faster speed. It is important to be able to play this accurately; don't be satisfied with getting MOST of the up and down strums in the right order. If it's not perfect, it will make learning any harder strums virtually impossible. Be sure that you can play the pattern many times in a row, without having to stop because of an incorrect strum.
This is a tricky concept, and may take newer guitarists some time to get used to. Try not to get frustrated; soon, it will become second nature, and you'll wonder how you ever had any sort of problem with this pattern at all.