Welcome to the forum
They are color coded and can be repaired with snug fitting rubber hose
The white part is called a vacuum manifold and its 2 halves can be separated
Its there from when the truck was assembled at the factory, so the dash panel can be plugged into the HVAC system easily
One half's vacuum hoses go to the Climate Control panel, the one that controls vent selection
The other half's hoses go out to the "vacuum motors" to open and close the doors, and that looks like the ones that were chewed
Just FYI the black hose runs to firewall and out to engine bay, it connects to Vacuum reservoir and engine vacuum
White hose is fresh air vent door AND runs out thru firewall where it changes to Grey hose color for heater bypass valve
As for the repair
Buy some smaller rubber hose(by the foot) that fits snugly over the colored hoses, you can cut a short section of one colored hoses to take into parts shop to get a good fit
Then you need to find the other ends of the colored hoses, which can be a pain
There are just 2 locations for the vacuum motors, one is a dual motor for the yellow and blue hoses
Diagram here:
https://www.ford-trucks.com/forums/attachment.php?attachmentid=517&stc=1
No clamps are needed, its Vacuum so pulls hose connections together doesn't push them apart, so even if you can only slide on the rubber hose a bit it will work
Defrost is No Vacuum used, which is why defrost vent is active now
Vacuum motors look like this:
https://i.ebayimg.com/images/g/NU8AAOSwKfFljvNr/s-l1200.webp
Just a spring in a vacuum container that will pull a vent door open/closed when vacuum is applied and the spring pushes it back with no vacuum