If you find the binomial distribution in question to be

x P(A=x)

0 125/216

1 75/216

2 15/216

3 1/216

and the geometric distribution in question to be

x P(B=x)

1 1/2

2 1/4

3 1/8

...

and we assume the two variables to be independent and random

then we can find the probability that A=B

by summing over x= 1,2 and 3

P(A=x) * P(B=x)

as B cannot = 0 and A cannot be > 3

ie

= 75/216 * 1/2 + 15/216 * 1/4 + 1/216 * 1/8 = 331/1728