Let x be the increase in price, and f(x) the weekly revenue.

f(x)="number of watches sold per week" times "price per watch" =(1200-40x)*(18+x)

Calculate the derivative f´(x) and solve the equation f´(x)=0. The solution of that equation, plus 18, is your answer. The result I get is $24.

You know the solution of f´(x)=0 is a maximum for the function f (rather than a minimum) by calculating the second derivative f"(x). It's negative, and that means it's a maximum.