An 18 ohm resistor and a 6 ohm resistor are connected in parallel to a battery, and the current in the 18 ohm resistor is found to be .45 amps. find the potential difference across the battery

With 0.45 amp flowing through an 18-ohm resistor, the voltage across it is

       V  =  I R  =  (0.45) x (18)  =  8.1 volts .

"But I asked for the battery voltage!  That's the voltage across the resistor."

The ends of the resistor are connected directly to the battery terminals.
They're the same voltage.

"But what about the 6-ohm resistor ?  Where does that figure in ?"

In parallel, it doesn't.  It's also connected directly across the battery,
and it has its own current. 

In parallel, neither resistor knows or cares whether or not there are
any other resistors present.  In parallel, it makes no dif.