An 18-mm-wide diffraction grating has rulings of 710 lines per millimeter. monochromatic light of wavelength 506 nm wavelength is incident normally on the grating. what is the largest angle from the centerline at which an intensity maximum is formed?

W= 18*10^-3m 
N= 18*710 ( because you have 710 slits per mm ) = 12780 
lambda = 506*10^-9 

The first step is to workout d. 
d = w/N 
d =18*10^-3m/12780 
d =1.41*10^-6m 

The second step is to work out the maximum number of m. 
Since sin (theta) = less than 1, then m*lambda/d = less then 1,
therefore m= less than d/lambda 
( I know thats confusing but trust me ) 
so m is less than 1.41*10^-6m/506*10^-9 
= 2.7 
Therefore use m = 2 

Lastly put it all into the formula
dsin (theta) = m*lambda so:
theta = sin^-1(m*lambda/d) 
theta = sin^-1(2*506*10^-9/1.41*10^-6m) 
theta = 45.95 degrees or 46 degrees