We can make two equations out of the information provided in the question:

Let's denote the two numbers by x and y:

x = y - 6

2y = 3x + 22

Let's take the variables to one side:

x - y = -6 --- equation I

3x - 2y = -22 --- equation II

Multiply Equation I by -2:

-2 (x - y = -6)

-2x + 2y = 12 --- equation III

Now, we can solve equation II and III as simultaneous equations:

3x - 2y = -22

-2x + 2y = 12

x + 0 = -10

x = -10

To find y, put the value of x into equation II:

3x - 2y = -22

3(-10) - 2y = -22

-30 - 2y = -22

-2y = -22 + 30

-2y = 8

y = 8/-2

y = -8/2

y = -4

Therefore, the two numbers are:

x = -10

y = -4

Let's denote the two numbers by x and y:

x = y - 6

2y = 3x + 22

Let's take the variables to one side:

x - y = -6 --- equation I

3x - 2y = -22 --- equation II

Multiply Equation I by -2:

-2 (x - y = -6)

-2x + 2y = 12 --- equation III

Now, we can solve equation II and III as simultaneous equations:

3x - 2y = -22

-2x + 2y = 12

x + 0 = -10

x = -10

To find y, put the value of x into equation II:

3x - 2y = -22

3(-10) - 2y = -22

-30 - 2y = -22

-2y = -22 + 30

-2y = 8

y = 8/-2

y = -8/2

y = -4

Therefore, the two numbers are:

x = -10

y = -4