To solve the equation Y + 4 7/10 = 5 8/15, we first need to convert the mixed numbers into improper fractions.

Y + 47/10 = 5 8/15

5 8/15 can be written as 5 + 8/15 = 5 1/2

Now, we can rewrite the equation as:

Y + 47/10 = 5 1/2

Next, we need to convert 5 1/2 into an improper fraction:

5 1/2 = 10/2 + 1/2 = 11/2

Now the equation becomes:

Y + 47/10 = 11/2

To solve for Y, we need to get the variables on one side of the equation. Let's first convert 11/2 to a decimal:

11/2 = 5.5

Subtracting 47/10 from both sides of the equation:

Y = 5.5 - 4.7

Y = 0.8

Therefore, the solution to the equation Y + 4 7/10 = 5 8/15 is Y = 0.8.