An experimental fix for the sound echo while Co-playing on Parsec was released with version 144-1. You can see information about the fix here
If this fix does not work for your use-case, however, you'll need to follow this more complicated manual setup.
You can first try to turn the host to push-to-talk on Discord. So that they only time Discord picks up audio is when you're talking. That way your friend won't hear himself.
More Involved Fix:
VB-Audio Cable is a program that allows you to emulate a sound device on your computer. You can download it here. The download file is a zip folder. You should unzip the folder and install the version of VB-Audio Cable for your computer. We're going to assume you're choosing the Win10 version. You should choose the correct 64 or 32-bit version for your computer as well.
INSTALLING VB-AUDIO CABLE
Right click on the correct version of VB-Audio Cable for your Windows 10 device and run it as administrator. If you do not have administrator privileges, this won't work.
SET VB-AUDIO CABLE AS DEFAULT SOUND DEVICE
Right click on the speaker icon in the bottom right corner of your task tray and then choose Playback devices.
Right click here
Choose Playback devices
In the Playback devices menu, choose Cable Input and Set as Default. Once you do that, click Apply.
If you did it right, there will now be a green check mark next to the VB-Audio Virtual Cable
SET YOUR SPEAKERS AS LISTENING DEVICE
This part is really important, or you won't be able to hear anything when someone connects. After setting the Default Playback Device, click on Recording, choose Cable Output, and then on Properties.
Now, choose the Listen tab and choose the Playback through this device. You should choose the sound device that your headphones or speakers play from. I use a headset, so my Realtek High Definition Audio (the motherboard sound device) is used to output sound. If you use speakers, they might be listed, and you should choose those. Just be aware that you may not hear if you switch to your headphones, and you'll need to go back into this step to set your motherboard sound device as the Playback.
LAST STEP - SET THE OUTPUT DEVICE IN DISCORD / SKYPE / TEAMSPEAK
We'll use Discord as the example because it's the best voice/text chat out there in my opinion. Click on your user settings in Discord. Choose Voice & Video. Once you're in that screen, choose your Output Device and set it equal to whatever speaker you choose in the step just before this as your Playback device on VB-Audio Cable, so you can hear people talking. If you don't do this, you'll hear nothing from Discord.
Yes, I am a monster, I use the light theme in Discord.
When you're done, Discord should look like this.
BEFORE YOU FINISH, RESTART PARSEC FROM TASK TRAY!