Spoiler for

Each step has a reverse step.

Arriving at (0, 0) means taking any three steps, along with their particular reverse steps.

Consider any of the steps taken. Its reverse must appear among the remaining five.

Consider any of the other four steps. Its reverse must appear among the remaining three.

Consider one of the remaining steps. The other must be its reverse.

All directions have 1/6 probability.

The probability of having a particular outcome in five chances, three chances and one chance,

multiplied together, is the desired result.

[1-(5/6)^{5}] [1-(5/6)^{3}] [1-(5/6)] = (4651/7776) (91/216) (1/6) = 423421/10077696 = 0.042.

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