One root of 3x^2 - 2(3b + 1)x + 4b = 0 is 8. Find the value of b.?

Just substitute x = 8. It will leave an equation in b.
3*(8^2) - (6b + 2)*8 + 4b = 176 - 44b = 0
b = 4

192 - 16 [ 3b + 1 ] + 4b = 0
192 - 48 b - 16 + 4b = 0
176 = 44 b
b = 4

3x² - 2x.(3b + 1) + 4b = 0 → given that one of the root is 8

3.(8)² - 2.(8).(3b + 1) + 4b = 0

192 - 48b - 16 + 4b = 0

176 - 44b = 0

44b = 176

b = 4