Let's solve the equation step by step.
The equation given is:
\[ 6y - 4y + 5y - 19 = 9 \cdot 2 - 2 \]
First, simplify both sides of the equation.
On the left side:
\[ 6y - 4y + 5y = (6 - 4 + 5)y = 7y \]
So, the left side simplifies to:
\[ 7y - 19 \]
Now, simplify the right side:
\[ 9 \cdot 2 - 2 = 18 - 2 = 16 \]
Now, we can rewrite the equation:
\[ 7y - 19 = 16 \]
Next, add 19 to both sides:
\[ 7y - 19 + 19 = 16 + 19 \]
This simplifies to:
\[ 7y = 35 \]
Finally, divide both sides by 7:
\[ y = \frac{35}{7} \]
So:
\[ y = 5 \]
The solution to the equation is \( y = 5 \).