Hi, lampros288,
Thanks for posting in the Apple Support Communities. I understand that after updating your iPhone to iOS 13 and your Apple Watch to watchOS 6, you're no longer able to answer calls on your Apple Watch, and neither you nor the other person can hear each other once on the call. I'm happy to help!
It sounds like you're able to receive the calls on the Apple Watch, just not answer them. The first thing I'd suggest in that instance would be to restart the Apple Watch: How to restart your Apple Watch - Apple Support, and its companion iPhone: Restart your iPhone, iPad, or iPod touch - Apple Support. This should address both the answering of calls and the audio while on them.
If the issues still continue, the steps in Get help with your Apple Watch - Apple Support may provide additional assistance.
Should you still need help after that, please get in touch with Apple Support directly: Contact Apple Support.
Have a great day.