This is actually a very difficult thing for a beginner on any instrument.
I share Heather S' opinion, that you're asking too much of yourself after one month of playing piano. I am a guitar player and I have noodled around on the piano, and I don't think anyone can do what you're talking about before they've truly internalized it.
If you're really keen to play exactly these two rhythms, here's how I would do it. I would start by working up to it very gradually. I would forget the piano and just try to tap these two rhythms simultaneously on my legs.
I would tap my RH slowly enough that I can comfortably tap triplets against it with my LH. Then, add the LH pattern. It would definitely help me to write down the rhythm for each hand. I could scale it to quarter notes (crotchets) in the RH. The LH would then be written in eighth-note (quaver) triplets.
I would take a break.
Then I would approach from the LH, where I tap it slowly enough that I can comfortably tap RH quadruplets against it, and tap the RH rhythm.
I would take another break.
I would switch back and forth with ample pauses, and gradually increase the tempi.
It will take a lot of focus and repetition, but when the rhythms flow comfortably and accurately at a range of tempi, I would then start applying them to an instrument.
(I have tried this more than once, but only half-heartedly, because I always got bored before I became adept at it. If I were more keen than I was before I would also try to find music with these rhythms in it to listen to regularly between practising sessions.)
If, on the other hand (pun possibly intended), I wanted to acquire general independence, I would just start learning songs from the classical piano repertoire, starting with really easy stuff. If I wanted an extra challenge in this regard, I would learn an easy piece and then switch the roles of each hand.