The problem didn't need to state that

because it says this:

Anyway:

We want the number to be as large as possible, so
we want the first digit, the thousands digit, to
be as large as possible.  We can't make it 9, because
the second digit is the largest digit.  So the largest
we can make the 1st digit is 8 and the 2nd digit 9.

So the number starts with "89". The last two digits have
to add up to the first digit. The largest two digit
number whose digits add up to 8 is 80, but we can't use
that since the 1st and 3rd digit can't be the same, so we 
pick the next largest two digit number with the sum of
digits 8, which is 71.

So the answer is 8971.

[Note, if they'd asked for the smallest 4-digit number instead
of the largest, the answer would have been 3412]

Edwin