Hey Friend,
The D major barre chord is going to come up in songs for you. It is located smack dab in the middle of the guitar neck, so there's no avoiding it. While the root 5 version (using the A shape triad in addition to the barre) is the more challenging of the two barre chord versions, you would be wise to work hard at this one.
To play a root 5 D major barre chord, barre the top five string at the fifth fret with your index finger. Using your ring finger, you're going to layer a second barre covering the second, third and fourth strings at the seventh fret. This gives you the A shape. Strum all five strings.
What you get is the D root note on the fifth string followed by A, D, F# and A, respectively.
I now this is a tough one, and all I can say is practice it. Getting a clean sound out of the second barre with your ring finger is awkward, but you will get it. It was a pain for me, too, and I eventually mastered that rotter (too strong?).
On the plus side, once you can play one root 5 barre chord, you can play them all. If you get frustrated in your practice, or you really need to use something because your band is waiting on you to learn a progression, use a D5 power chord. It'll fill the gap until you have that barre down.
The root 6 barre is probably not going to be used as much simply because of its location on the neck. We play this on at the tenth fret, so if you're on an acoustic guitar this starts to get a bit more challenging to play, just because of the proximity to the body.
Barre all six strings at the tenth fret with your index finger. Place your middle finger on the third string, eleventh fret, you ring finger on the fifth string, twelfth fret and the pinky on the fourth string, twelfth fret. What you've got is an E shape chord on top of the barre with notes D, A, D, F#, A and D from strings six to one.
The exercises walk you through building out the chord note by note, so refer to those to get the fingering right, or to refresh your memory if you're a little rusty.
Peace~
Dave | 
