To solve this equation, we can start by simplifying both sides by finding a common denominator.
\(\frac{y + 1}{2} - \frac{2y - 1}{3} = 4\)
Multiplying the first term by 3 and the second term by 2 (the least common multiple of 2 and 3), we get:
\(\frac{3(y+1)}{6} - \frac{2(2y-1)}{6} = 4\)
Simplifying this gives:
\(\frac{3y + 3 - 4y + 2}{6} = 4\)
Combining like terms:
\(\frac{-y + 5}{6} = 4\)
Multiplying both sides by 6:
\(-y + 5 = 24\)
Subtracting 5 from both sides:
\(-y = 19\)
Finally, multiplying both sides by -1 to solve for y:
\(y = -19\)
Therefore, the solution is y = -19.