Hydrogen atoms give out a line when the electron jumps from the level n = 6 to n = 4…

Step 1. Wave number. $\dfrac{1}{\lambda} = 1.097 \times 10^{7}\ \text{m}^{-1} \times \left(\dfrac{1}{16} - \dfrac{1}{36}\right) = 1.097 \times 10^{7}\ \text{m}^{-1} \times 0.03472 = 3.81 \times 10^{5}\ \text{m}^{-1}$.

Step 2. Wavelength. $\lambda = \dfrac{1}{3.81 \times 10^{5}\ \text{m}^{-1}} = 2.63 \times 10^{-6}\ \text{m}$, about $2625\ \text{nm}$.

Region. It is longer than $700\ \text{nm}$, so it is infrared. It belongs to the Brackett series.