Let the three numbers be: X, Y, Z.

The sum of the 3 even numbers is 64.

X + Y + Z = 64 --------------------- (1)

The quotient of 1 more than the second number and 2 less than the first number is 0.5.

(Y + 1) / (X - 2) = 0.5 = 1/2

cross-multiplying,

2Y + 2 = X - 2

2Y = X - 4 ------------------------ (2)

Quotient of 4 more than twice the second number and 2 less than the third number is 2. What are these three numbers?

(2Y + 4) / (Z - 2) = 2

2Y + 4 = 2Z - 4

2Y = 2Z - 8

Y = Z - 4 ------------------------ (3)

Substituting for X = 2Y + 4 from (2) into (1),

2Y + 4 + Y + Z = 64

3Y + Z = 60 -------------------- (4)

Substituting for Y = Z - 4 from (3) into (4),

3Z - 12 + Z = 60

4Z = 72

Z = 18

Using (3), Y = 14

Using X = 2Y + 4 from (2), X = 32

**The three numbers are: X = 32, Y = 14, Z = 18**