Solution: The surface area of a regular hexagonal prism consists of the area of the two hexagonal bases and the six triangular lateral faces. Each face is equilateral with side length $ s = 4 $ cm.

["The Surface Area of a Regular Hexagonal Prism: A Step-by-Step Solution", "Understanding the surface area of a regular hexagonal prism is essential for students of geometry, architecture, and engineering. This 3D shape combines symmetrical hexagonal bases with rectangular (often triangular) lateral faces, making it a fascinating subject for solving surface area problems with clarity and precision.", "In this article, we’ll explore the formula for the surface area of a regular hexagonal prism, calculate it step-by-step, and clarify the role of equilateral triangular lateral faces with side length $ s = 4 $ cm.", "---", "### What Is a Regular Hexagonal Prism?", "A regular hexagonal prism is a polyhedron with two parallel, regular hexagonal bases connected by six rectangular (in standard form) but here — in the regular case — six equilateral triangular lateral faces formed by connecting corresponding vertices of the two hexagons. While equilateral bases are key, lateral faces are typically equilateral only in special configurations, but in a regular hexagonal prism, they are regular hexagons collapsed into six equilateral lateral surfaces due to symmetry.", "However, note: in standard terminology, a regular hexagonal prism has two regular hexagonal bases and six rectangles. But when the lateral faces are equilateral triangles, the prism is actually a triangular hexagonal prism in misnomer — rather, the intended meaning is a regular prism with regular hexagonal bases and equilateral (equal-sided, equal-angled) lateral faces, meaning the shape becomes a regular hexagonal bipyramid only if faces meet at a peak. Clarification confirms: for surface area, we compute based on two regular hexagonal bases and six equilateral triangular lateral faces — a shape known as a regular hexagonal prism only if lateral faces are rectangles, but here, equilateral lateral surfaces suggest a redefined prism.", "For mathematical clarity, we assume the intended figure is a regular hexagonal prism with two regular hexagonal bases and six equilateral lateral faces, implying that each lateral face is an equilateral triangle formed by connecting vertices of the top and bottom hexagons — this only happens when vertical height equals side length $ s $, and angles align perfectly.", "But in standard geometry, such a construction is only possible if the lateral edges are equal and the top hexagon is scaled — however, for simplicity and despite complexity, we interpret the problem as:\nA regular hexagonal prism with equilateral triangular lateral faces, implying symmetry and equal edge lengths, where each lateral edge and base edge is $ s = 4 $ cm.", "This defines a special case: a right regular hexagonal prism where lateral faces are equilateral triangles — achievable only if the distance between corresponding vertices equals the base edge $ s $. Thus, height $ h $ of prism equals $ s = 4 $ cm, and each lateral face forms an equilateral triangle.", "---", "### Formula for Surface Area", "The total surface area $ A $ of a prism is:\n[\nA = \ ext{Area of two bases} + \ ext{Area of lateral faces}\n]", "For a regular hexagonal prism with side length $ s $:", "- Area of one regular hexagonal base:\n[\nA_{\ ext{base}} = \frac{3\sqrt{3}}{2} s^2\n]", "- There are two bases:\n[\n2 \ imes \frac{3\sqrt{3}}{2} s^2 = 3\sqrt{3} s^2\n]", "- Lateral surface area:\nSix equilateral triangular faces, each with side length $ s $.\nArea of one equilateral triangle:\n[\nA_{\ ext{triangle}} = \frac{\sqrt{3}}{4} s^2\n]\nSix such triangles:\n[\n6 \ imes \frac{\sqrt{3}}{4} s^2 = \frac{6\sqrt{3}}{4} s^2 = \frac{3\sqrt{3}}{2} s^2\n]", "---", "### Step-by-Step Calculation", "Given $ s = 4 $ cm:", "#### 1. Area of one hexagonal base:\n[\nA_{\ ext{base}} = \frac{3\sqrt{3}}{2} (4)^2 = \frac{3\sqrt{3}}{2} \ imes 16 = 24\sqrt{3} , \ ext{cm}^2\n]", "#### 2. Total area of two bases:\n[\n2 \ imes 24\sqrt{3} = 48\sqrt{3} , \ ext{cm}^2\n]", "#### 3. Area of one equilateral triangle:\n[\nA_{\ ext{triangle}} = \frac{\sqrt{3}}{4} (4)^2 = \frac{\sqrt{3}}{4} \ imes 16 = 4\sqrt{3} , \ ext{cm}^2\n]", "#### 4. Total lateral surface area:\n[\n6 \ imes 4\sqrt{3} = 24\sqrt{3} , \ ext{cm}^2\n]", "#### 5. Total surface area:\n[\nA = 48\sqrt{3} + 24\sqrt{3} = 72\sqrt{3} , \ ext{cm}^2\n]", "---", "### Why This Formula Matters", "This problem illustrates key geometric principles:\n- Breakdown of complex surfaces into standard shapes.\n- Application of equilateral triangle area formula.\n- Understanding how side length governs total surface area.\n- Recognizing symmetry in prisms enhances computational accuracy.", "---", "### Final Answer", "The surface area of a regular hexagonal prism with side length $ s = 4 $ cm, composed of two regular hexagonal bases and six equilateral triangular lateral faces, is:", "[\n\boxed{72\sqrt{3} , \ ext{cm}^2}\n]", "This structured approach ensures precise computation and deep comprehension of 3D geometry fundamentals.", "---", "### Key Takeaways\n- Surface area = sum of base areas + lateral area\n- Equilateral triangle area: $ \frac{\sqrt{3}}{4} s^2 $\n- Regular hexagon area: $ \frac{3\sqrt{3}}{2} s^2 $\n- Consistent edge lengths (here $ s = 4 $ cm) simplify calculations\n- Ideal for math education and real-world applications like packaging design and architecture", "---", "Keywords: Surface area of a hexagonal prism, regular hexagonal prism surface area, equilateral triangle area, geometry problem solution, side length s = 4 cm, 3D geometry, hexagonal bases, triangular lateral faces, math tutorial, high school geometry."]