Let's analyze the equation and determine how many solutions it has. The equation is:

$2 - 4y - 6y = -9y + 6$

Step 1: Combine like terms on both sides.

On the left side of the equation:

$2 - 4y - 6y = 2 - 10y$

So the equation becomes:

$2 - 10y = -9y + 6$

Step 2: Move all terms involving $y$ to one side.

Add $10y$ to both sides:

$2 = y + 6$

Step 3: Solve for $y$.

Subtract 6 from both sides:

$2 - 6 = y$

$y = -4$

Conclusion:

There is one solution to this equation, and it is $y = -4$.

Would you like more details or have any other questions?

Here are 5 related questions:

1. How can we verify that $y = -4$ is the correct solution?
2. What are the steps to solve similar linear equations?
3. How do equations with no solution differ from this one?
4. Can you explain what happens when the variables cancel out on both sides?
5. What is the difference between having one solution, no solution, or infinite solutions?

Tip: Always combine like terms first to simplify the equation before solving for the variable.