is the transmission operating correctly? if it is , that hose is most likely a vent tube,

On the Chassis, next to the fuel tank. Follow the hose out of the tank.

A dual line system is a safety item. If a brake line/brake hose lets go you will still have brakes on one axle, you may not stop on a dime but it will stop you. A single line system will leave you with out any brakes at all if one brake line/hose lets go. American made cars have had a dual line systems since 1968.

Portable Air Conditioners can come with one hose or two hoses. A two hose(Dual Hose) unit is a little more costly, but more efficient than a single hose.

Please see our webpage for more info:

http://www.bestportableairconditionerratings.com/what-to-look-for-when-buying-a-portable-air-conditioner/

Unfortunately, the easiest way to change the hose (firewall connections) is from under the car. If your Achieva has the dual hose with the black valve across both lines, make sure you go to the dealer for the replacement. It's important for proper operation. Replacing with regular heater hose will cause problems down the road.