To solve this problem, first convert all mixed numbers to improper fractions:

4 13/18 = (418 + 13)/18 = 85/18
3 7/9 = (39 + 7)/9 = 34/9

Now multiply the two fractions:

(85/18 - 34/9) * (1/2 - 4/14)

= (85/18 - 34/9) (7/14 - 4/14)
= (85/18 - 34/9) 3/14
= (85/18 - 34/9) 3/14
= (85/18 - 68/18) 3/14
= (17/18) * 3/14
= 51/252
= 17/84

Therefore, (4 13/18 - 3 7/9) * (1/2 - 4/14) = 17/84.