To solve for $y$ in the equation $6x - 2y = 14$, follow these steps:

Step 1: Isolate the term with $y$

Start by subtracting $6x$ from both sides:

$-2y = 14 - 6x$

Step 2: Solve for $y$

Now, divide both sides of the equation by $-2$ to isolate $y$:

$y = \frac{14 - 6x}{-2}$

Step 3: Simplify the right-hand side

Simplify the expression:

$y = \frac{14}{-2} - \frac{6x}{-2}$

$y = -7 + 3x$

So the solution is:

$y = 3x - 7$

Would you like more details or clarification? Here are some related questions:

1. What would happen if the equation was $6x + 2y = 14$?
2. How would you solve a system of equations involving this one?
3. Can this method be applied to any linear equation?
4. How would you graph the equation $y = 3x - 7$?
5. How do you check the solution for $y = 3x - 7$ in the original equation?

Tip: When solving for a variable in a linear equation, always aim to isolate the variable by using inverse operations like addition, subtraction, multiplication, or division.