The double paradiddle is similar to a single paradiddle, in which what you say sounds like what you're going to hear when you play it. Dou-ble pa-ra-did-dle, dou-ble pa-ra-did-dle. If you know anything about the term "diddle," we're talking about a double. It would basically be a right-left-right-left-right-right for the double, followed by a left-right-left-right-left-left for the double on the left side. These do alternate. You're going to start with your strong hand, and you're going to end up on your weak hand as it alternates.
Another way of playing this, also, is to bring out the accent on the beginning of each of your single-noted groupings. DOU-ble PA-ra-did-le. DOU-ble PA-ra-did-le. I'll play it now slowly so you can hear it. Then I'll speed it up so you can hear it in time.
If you've studied a paradiddle at all, there are ways of playing that rudiment with an accent on the down beat, or everything accented or non-accented, where you just play everything evenly. The double paradiddle could be played the same way, with the accents I just played, or every note the same volume. Either way, you want to make sure that they alternate, and that you have that diddle with a double on the end of each grouping that you play.