Only move in three directions the entire game when possible. (Preferable up-left-right, but concept is the same.)
On the single direction side (e.g top), always try to keep the biggest number in the corner (e.g top left) and fill upward from the other corner. To do this if the top left is a 512... Then a 128... Then a 64... Then a blank. Try not to shift right. It could drop a 2 in the top left corner breaking the rule. That would require you to get the 2 up to a 512 to continue the pattern.
I will post a picture of the process.