Cool question! There’s a lot of ways you can accomplish this.
If you’re only modeling sounds in four directions, then the issue is distinguishing between sound sources that are ahead or behind. The simplest thing you could do is apply a lowpass filter to sounds behind the player so they sound muffled. It depends on your sound design, but a cutoff frequency of 2k Hz is a good starting point. Gain reduction might help too. Research acoustic shadow for more info.
For full 2D or 3D audio spatialization you might want to look into binaural rendering or a head-related transfer function (HRTF). By simulating human hearing in a physical space we can create a familiar analog to real life. Your game engine or audio library should have tools to get you started with this.