# A Standard Walk on the Coordinate Space

**Discrete Mathematics**Level 4

Daniel is standing on the origin in the coordinate **space**. He walks either up, down, left, right, forwards, or backwards one unit each second, each with equal probability. After 6 seconds, the probability he is back on the origin can be expressed as \(\dfrac{p}{q}\) for positive coprime integers \(p,q\). Find \(p\).