To solve this operation, we need to first convert the mixed fractions to improper fractions.

4 1/2 = 9/2
0.7 = 7/10
1 85/20 = 25/20 + 85/20 = 110/20

Now we can perform the multiplication:

(9/2 - 7/10) (110/20)
= (9/2 - 7/10) (11/2)
= ((910 - 72) / 10) (11/2)
= (90 - 14) / 10 11/2
= 76 / 10 11/2
= 38/5 11/2
= (3811) / (52)
= 418 / 10
= 41.8

Therefore, (4 1/2 - 0.7) * (1.85 + 3/20) is equal to 41.8.