Waste water keeps back up from chicken sink

[BlueSky16]

Hi, waste water won't be drained out from my left and right kitchen sink. I tried to turn on the garbage disposal but water was still back up. I opened PVC hoses under the sink to check but they were all clear. I guess maybe the hose that takes water out of the sink/house somehow gets stuck, but I am not sure what I should do.
Can you please help? Thank you

 

[Twowaxhack]

You need to have a drain cleaning company clean the drain line with a drain machine. Commonly referred to as a drain snake

 

[Jeff Handy]

Just remove the chickens from your sink.