I have been working on some hats for only a little while and I saw a pattern that has on there to work the pattern in garter stitch. Is it possible to do the pattern on double pointed needles?
Yes. Assuming you still intend to work in the round, you'll need a stitch marker for the start of the row. You'll need to ironicly alternate between plain and purl each row. Otherwise you'll just get stocking stitch.
If you intend to work flat which given the pattern is garter it probably is. I would recommend cables over DPNs.
Just like in flat knitting (assuming that you're knitting in the round) you need to alternate between purl and knit stitches each round, so you could either knit by the pattern, purling all knits and kitting all purls, or you could use a stitch marker (at least 1 stitch away from the end of the needle) to mark where you need to switch stitches.
An extra option that you have is that you could also knit it flat and join it in the round with mattress stitch.