Which of these points lies on the line described by the equation below?

To determine which point lies on the line described by the equation \( Y - 4 = -2(x - 6) \), we can start by rewriting the equation in slope-intercept form ( \( Y = mx + b \) ).

1. Start with the given equation:
\[
Y - 4 = -2(x - 6)
\]

2. Distribute on the right side:
\[
Y - 4 = -2x + 12
\]

3. Add 4 to both sides to solve for \( Y \):
\[
Y = -2x + 16
\]

Now we have the equation of the line in slope-intercept form: \( Y = -2x + 16 \).

Next, we'll substitute each of the given points into the equation to see if they satisfy it.

**Option A: (4, 6)**
\[
Y = -2(4) + 16 = -8 + 16 = 8 \quad \text{(not 6)}
\]

**Option B: (6, 4)**
\[
Y = -2(6) + 16 = -12 + 16 = 4 \quad \text{(correct)}
\]

**Option C: (-4, -6)**
\[
Y = -2(-4) + 16 = 8 + 16 = 24 \quad \text{(not -6)}
\]

**Option D: (-6, -4)**
\[
Y = -2(-6) + 16 = 12 + 16 = 28 \quad \text{(not -4)}
\]

The only point that satisfies the equation is **B. (6, 4)**.