If I multiply 51,249,876 by 3 (thus using all the nine digits once, and
once only), I get 153,749,628 (which again contains all the nine digits
once). Similarly, if I multiply 16,583,742 by 9 the result is
149,253,678, where in each case all the nine digits are used. Now, take
6 as your multiplier and try to arrange the remaining eight digits so as
to produce by multiplication a number containing all nine once, and once
only. You will find it far from easy, but it can be done.