The pH of a 0.1 M solution of sodium hydroxide is approximately 13. Sodium hydroxide dissociates almost completely in water, so a 0.1 M solution has a hydroxide-ion concentration of about 0.1 M. At 25 °C, its pOH is 1, and because pH + pOH = 14, the pH is 13.
Sodium hydroxide, commonly called lye or caustic soda, is a strong base. The sodium ions do not significantly affect the acid-base calculation; the hydroxide ions are responsible for the solution's alkalinity. This is different from a weak base, which would dissociate only partly and require an equilibrium calculation.
The value assumes an ideal dilute solution and the conventional 25 °C pH scale. At higher concentrations, activity effects can make the measured or thermodynamic pH differ slightly from the simple calculation. The answer is not 14 because that corresponds approximately to a 1 M hydroxide solution under the same simplified assumptions, while pH 7 describes neutral water.