This problem is easier if you draw a picture. Let me see if this works here!
 
                        start
<-------18mph----|----12mph------>
{                                                  }
{ ---------246 miles------------------}
 
Ok. So, consider the situation after the first hour. Where will the trains be? The first train has gone 18 miles west, and the second train has gone 12 miles east (I'm just picking directions). They'll be 18+12=30 miles apart. Ah, so every hour the distance is 30 miles! Now you can use your typical Rate times Time = Distance formula, using a single rate, 30 miles per hour, which is the combined rate and is the rate at which the distance between the trains increases, every hour.
 
So: RT=D. Solve this for T, since that's our unknown. You get T=D/R. Substitute R=30 and D=246.
 
T = 246/30; T=8.2 hours   If they want it in hours and minutes, it's 8 hours and 12 minutes.