I'm a beginner with Max and what I'm trying to do is take the the audio input signal going into my Arduino and hear the receiving audio playing through Max. There's a photo below of the patch that I'm working with. If anyone knows how to do this, It would be much appreciated.
You need to write firmware for your arduino that gets values from the ADC and sends them to its serial port.
Problem: the arduino sketch firmware environment is especially ill-suited for such real-time tasks. I find it advisable not to try and mix native timer ISRs that shove data through DMA to the serial port (which is what you'd need) with arduino sketches, which try to make the microcontroller look like a fully blown system with little direct control over hardware.
Second problem: your serial port is configured to, best case, give you 9600 bd, which probably corresponds to but 1200 Bytes per second - simply far far too little for recognizable audio.
Last problem: you haven't shared any hardware notes with us, so I suspect you've thought about none of the analog problems.
I think you want a sound card. Buy an external (usb) sound card. They are cheaper than Arduinos.