To solve each of these equations, we need to isolate the variable indicated. Let's solve them one by one:

3/8y = 2.25

First, let's multiply both sides by 8/3 to eliminate the fraction:
y = 2.25 * 8/3
y = 6

8.4 : x = 2 1/3

To solve for x, we first convert the mixed number to an improper fraction:
2 1/3 = 7/3

x = 8.4 / 7/3
x = 8.4 * 3/7
x = 3.6

x : 5/9 = 3.6

x = 3.6 * 5/9
x = 2

y : 1.2 = 1 2/3

To solve for y, we first convert the mixed number to an improper fraction:
1 2/3 = 5/3

y = 1.2 * 5/3
y = 2

0.6x = 9/20

x = (9/20) / 0.6
x = 9/20 * 1/0.6
x = 0.75

5/6y = 0.5

y = 0.5 / 5/6
y = 0.5 * 6/5
y = 0.6

Therefore, the solutions are:

y = 6x = 3.6x = 2y = 2x = 0.75y = 0.6