#### Answer

The solution is:
$$y = 20$$
To determine if the solution is correct, we plug $20$ in for $y$ into the equation to see if both sides of the equation are equal:
$$5(2(20) - 3) - 1 = 4(6 + 2(20))$$
We can simplify what we have in parentheses:
$$5(40 - 3) - 1 = 4(6 + 40)$$
$$5(37) - 1 = 4(46)$$
We simplify using order of operations to multiply first:
$$185 - 1 = 184$$
We then do the subtraction:
$$184 = 184$$
We see that the solution is correct because both sides of the equation are equal.

#### Work Step by Step

To solve, we have to simplify the equation first.
We distribute the terms in parentheses:
$$10y - 15 - 1 = 24 + 8y$$
We now move the $y$ terms to one side of the equation by subtracting $8y$ from both sides of the equation:
$$2y - 15 - 1 = 24$$
We want constants on the other side of the equation, so we add both $15$ and $1$ to both sides of the equation:
$$2y = 40$$
We now isolate $y$ by dividing both sides by $2$:
$$y = 20$$
To determine if the solution is correct, we plug $20$ in for $y$ into the equation to see if both sides of the equation are equal:
$$5(2(20) - 3) - 1 = 4(6 + 2(20))$$
We can simplify what we have in parentheses:
$$5(40 - 3) - 1 = 4(6 + 40)$$
$$5(37) - 1 = 4(46)$$
We simplify using order of operations to multiply first:
$$185 - 1 = 184$$
We then do the subtraction:
$$184 = 184$$
We see that the solution is correct because both sides of the equation are equal.