In these types of Weighted Average questions, you can always use the Average Formula (as Bunuel showed). There are often ways to solve the problem by doing "relationship math" - it's essentially the same math (but in a different order) and might save you some time if you're comfortable with the concepts involved.
Here, we know that the average of 10 vehicles is 12 tons. In real simple terms, we COULD say that we have 10 vehicles that weight 12 tons EACH. Adding another vehicle raises the AVERAGE WEIGHT of ALL the vehicles 2.4 tons. We're asked for the weight of this extra vehicle.
So, if we raise each of the 10 vehicles 2.4 tons, then each would weight 14.4 tons --> 10(+2.4 tons) = 24 extra tons
To keep the overall average at 14.4 tons, we have to include that weight in the extra vehicle too -->14.4 tons + the increase in the other vehicles.
This gives us 14.4 + 24 = 38.4 tons
GMAT assassins aren't born, they're made,