Answer
360 nm.
Work Step by Step
An intensity maximum occurs when $d sin \theta=m \lambda$, and third-order means m = 3.
The longest observable wavelength is the one that gives an angle of 90 degrees, so the sine is 1.
Find d from the information that there are 92000 slits/m.
$$d=\frac{1}{920000slits/m}=1.087\times10^{-6}m$$
Now find the longest wavelength.
$$\lambda=\frac{d sin \theta}{m}=\frac{(1.087\times10^{-6}m)(1) }{3}=3.6\times10^{-7}m $$
