To solve the equations:

1) 2 1/7 * 2.5 = 8.4 : 7x

Converting 2 1/7 to an improper fraction:
2 1/7 = 15/7

15/7 * 2.5 = 37.5/7 = 5.357
So, the equation becomes:
5.357 = 8.4 : 7x

To solve for x:
8.4 / 5.357 = 1.567

7x = 1.567
x = 1.567/7
x = 0.224

2) 7 1/3 : 1 5/6 = 0.6x : 0.75

Converting 7 1/3 and 1 5/6 to improper fractions:
7 1/3 = 22/3
1 5/6 = 11/6

22/3 : 11/6 = 0.6x : 0.75

Calculating the division of the fractions:
(22/3) / (11/6) = 44/3 / 11/6 = 8

So the equation becomes:
8 = 0.6x : 0.75

To solve for x:
0.6x = 8 * 0.75
0.6x = 6.0
x = 6.0 / 0.6
x = 10.0

Therefore, the solutions are:
1) x = 0.224
2) x = 10.0