To solve the given equation, we first need to simplify both sides of the equation step by step:

Start with the left side of the equation: X - (8/15)X = 4 1/5
Simplify this to get: (15/15)X - (8/15)X = 21/5
Combine like terms: (7/15)X = 21/5
Multiply both sides by 15 to get rid of the fraction: X = 21/5 * 15/7 = 3

Now move on to the right side of the equation: (7 1/10)y - y
Simplify this to get: (71/10)y - y
Combine like terms: (61/10)y
This simplifies to: (61/10)y

Now simplify the right side of the equation further: 6/10 = 3 5/100
Convert the fraction to a mixed number: 6/10 = 3/5
Now substitute this back into the equation: (61/10)y = 3 5/100
Convert 3 5/100 to an improper fraction: 315/100
Now we have: (61/10)y = 315/100
Simplify by dividing both sides by 61/10: y = 315/100 / 61/10
y = 315/100 * 10/61
y = 3150/6100
y = 315/610

Therefore, the solutions to the given equation are X = 3 and Y = 315/610.