Thank you to those of you who sent in solutions - sorry that we can't mention everyone. Cong from St Peters RC School in Aberdeen shaded the hexagon grid which helped him to answer the question:

Cong says:

The multiples of $2$ are highlighted by blue. The multiples of $5$ are highlighted by yellow.
The $6$ possible paths that you could take are:
$0$ to $2$ to $5$
$0$ to $10$ to $25$
$0$ to $10$ to $5$
$0$ to $14$ to $15$
$0$ to $18$ to $15$
$0$ to $18$ to $20$

Well done also to Liam and Daniel from Troon County Primary School, and Erika from the Chinese International School (to name just a few).