Remove all dominoes that have a five or a
six on them.

Use only the fifteen that remain, where the
double-four is the highest.

In how many different ways may the fifteen dominoes be arranged in a straight
line in accordance with the simple rule of the game that a number must always be
placed against a similar number that is, a four against a four, a blank against
a blank, and so on?

Left to right and right to left of the same arrangement are
to be counted as two different ways

See answer