The region y ≥ 2x has a boundary line through the origin, so the origin cannot be the test point…

Step 1. Test each point.

• $(1, 3)$: $3 \ge 2$, true.
• $(2, 1)$: $1 \ge 4$, false.
• $(3, 6)$: $6 \ge 6$, true, and it is on the line.
• $(4, 7)$: $7 \ge 8$, false.
• $(0, 0)$: $0 \ge 0$, true, and it is on the line.
• $(-1, -1)$: $-1 \ge -2$, true.

Step 2. Count. Four points satisfy the inequality. Two of them, $(3, 6)$ and $(0, 0)$, are exactly on the line.