Choice B is the correct answer. Let's analyze each system:

System I: $y = 6x + 2$ and $y = 6x - 5$

• Same slope (6), different intercepts (2 and -5)
• Parallel lines → No solution

System II: $y = 6x + 2$ and $3y = 18x + 6$

• Divide second by 3: $y = 6x + 2$
• Same line → Infinitely many solutions ✓

System III: $y = 6x + 2$ and $y = -6x + 2$

• Different slopes (6 and -6)
• Intersecting lines → One solution

Conclusion: Only System II has infinitely many solutions.

💡 Strategic Tip: For infinitely many solutions, equations must represent the exact same line (same slope, same intercept).

Choice A is incorrect because System I has no solution (parallel lines).

Choice C is incorrect because System III has one solution (different slopes).

Choice D is incorrect because System I has no solution.