Step 1: Find slope of line through \((-1,4)\) and \((0,6)\).
Formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} \)
\( m = \frac{6 - 4}{0 - (-1)} = \frac{2}{1} = 2 \).

Step 2: Find slope of line through \((3,y)\) and \((2,7)\).
\( m = \frac{y - 7}{3 - 2} = y - 7 \).

Step 3: Since lines are parallel, their slopes are equal:
\( y - 7 = 2 \).

Step 4: Solve for \( y \):
\( y = 2 + 7 = 9 \).