Ok so in this problem we need to multiply the probability of both events together to find how likely it is that the die actually rolled a 4.
[tex] \frac{2}{3} [/tex] is the amount of times he speaks the truth, so we multiply that by [tex] \frac{1}{6} [/tex] for the die, because the die has 6 sides
[tex] \frac{1}{6} [/tex] × [tex] \frac{2}{3} [/tex] = [tex] \frac{2}{18} [/tex]
Simplify to get [tex] \frac{1}{9} [/tex]. Hope this helped!
