Answer
The thickness of this book is equal to $5.8 \times 10^{3}$ light-years.
Work Step by Step
1. Since each page must have a thickness of 0.0036 in., and the book has $6.022 \times 10^{23}$ pages. The total thickness of the book, in inches, is:
$$0.0036 \space in./page \times \frac{6.022 \times 10^{23} \space pages}{1 \space book} = 2.17 \times 10^{21} \space in./book$$
2. Now we need to find a way to convert from inches to light-years:
$$1 \space light-year = 3.00 \times 10^8 \space m/s \times \frac{60 \space s}{1 \space min} \times \frac{60 \space min}{1 \space h} \times \frac{24 \space h}{1 \space day} \times \frac{365 \space day}{1 \space year}$$
$$1 \space light-year \approx 9.46 \times 10^{15} \space m$$
$$9.46 \times 10^{15} \space m \times \frac{1 \space in.}{0.0254 \space m} = 3.72 \times 10^{17} \space in.$$
3. Finally, find the amount of light-years in this book:
$$Thickness = \frac{1 \space light-year}{3.72 \times 10^{17} \space in.} \times \frac{2.17 \times 10^{21} \space in.}{1 \space book} = 5.8 \times 10^3 \space light-years/book$$
