To simplify this expression, we can use the properties of logarithms:

log_b (M * N) = log_b M + log_b Nlog_b (M / N) = log_b M - log_b N

Using these properties, we can rewrite the expression as follows:

2log4 6 + log4 5/9 - log4 5
= log4 (6^2) + log4 (5/9) - log4 5
= log4 36 + log4 (5/9) - log4 5
= log4 36 + log4 5 - log4 9 - log4 5
= log4 36 - log4 9
= log4 (36/9)
= log4 4
= 1

Therefore, the simplified expression is 1.