Choice B is the correct answer. Finding maximum integer values requires solving and identifying boundaries.

1. Multiply by 5: $5 \cdot \frac{4x+8}{5} \leq 5 \cdot 4$, giving $4x + 8 \leq 20$
2. Subtract 8: $4x \leq 12$
3. Divide by 4: $x \leq 3$
4. Greatest integer: Since $x \leq 3$, maximum is exactly 3

?�� Strategic Tip: For $\leq$ inequalities, the boundary value itself is included in the solution set.

Choice A is incorrect because while $x = 2$ satisfies the inequality, it's not the GREATEST integer. Choice C is incorrect because$x = 4$ does not satisfy $x \leq 3$ (4 is greater than 3). Choice D is incorrect because$x = 5$ exceeds the solution range.