I'll try to explain:

we have to make abcd * efghi as large as possible

Multiplying this out and collecting together the powers of 10 this is equal to:

10,000,000ae

+1,000,000(be + af)

+100,000(ag + bf + ce)

+10,000(ah + bg + cf + de)

+1,000(ai + bh + cg + df)

+100(bi + ch + dg)

+10(ci + dh)

+ di

Considering the largest (most important) multiple of 10 we see that ae governs its multiplier value, therefore a and e must be 8 and 9, however a appears in more powers of 10 than e, so we will get the biggest answer if a=9, e=8. ie answer = 9bcd * 8fghi

Next most important power of 10 is 1,000,000(8b + 9f) we can see that 7 and 6 must come in here and we get the largest multiplier by multiplying 8*6, 9*7 i.e b=6, f=7, now we have 96cd * 87ghi

Next power of 10 is 100,000(9g + 42 + 8c), 5 and 4 must come in here and this will be largest if g=5, c=4, now we have 964d * 875hi

Considering d and i, it is clear that these have the least impact, so must be where we allocate 1 and 2. i affects powers of 10 up to 1,000, whereas d affects them up to 10,000 so it is best if d=2, i=1: now we have 96c2 * 87gh1

Next smallest numbers (3 and 4) look like they must go in c and h, c affects higher numbers than h, so c=4, h=3 will yield the largest product: 9642 * 87g31

Filling in the missing 5: 9642 * 87531 = 843973902 is the largest product