# Archit needs to go home!

Starting at $$(2,2)$$, an object moves in the coordinate plane via a sequence of steps, each of length 1. Each step is left, right, up or down, all four being equally likely. If the probability that the object reaches to $$(4,4)$$ in 6 or fewer steps is $$\dfrac a{64}$$, then what is the value of $$a$$?

Note that the favorable path for finding the probability are those in which object stops as soon as it reaches $$(4,4)$$.

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