We see that:
zw/(2z - 3w)
= [(3 - j)(1 + 3j)]/[2(3 - j) - 3(1 + 3j)]
= (3 + 9j - j - 3j^2)/[(6 - 2j) - (3 + 9j)], by FOILing the numerator
= (6 + 8j)/(3 - 11j), by simplifying (note that j^2 = -1).

At this point, you can rationalize the numerator and simplify to get:
(6 + 8j)/(3 - 11j) = -7/13 + (9/13)j.

Thus:
Im[zw/(2z - 3w)] = Im[-7/3 + (9/13)j] = 9/13.

I hope this helps!

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