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