578 * 6 = 3468 (only tried 3digit numbers; that's the only one)
Easy enough with a looper program, like:
loop a from 1 to 7
loop b from a+1 to 8
loop c from b+1 to 9
u = 100a + 10b + c
v = u*6
are v's digits in ascending order?
As far as a "method" goes, you'd need to start by setting up "u" something like (if 3digit number):
u = 100a + 10(a+w) + a+w+x
So u = 111a + 11w + x where 8>a>0 and a+w+x<10
Does 666a + 66w + 6x = an ascending 3digit or 4digit number?
Perhaps someone here with "number theory expertise" can help you further...I can't