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The minimum dimensions of a hearth are critical for safety and effective fire containment. The hearth must extend beyond the firebox opening to prevent heat from escaping and to protect surrounding materials from the potential of catching fire. In this scenario, the firebox measures 4 feet wide and 2 feet tall.

Hearth dimensions are often determined by specific formulas outlined in building codes, which generally require the hearth's width to extend at least 1 foot beyond each side of the firebox. In this case, for a 4-foot wide firebox, the total minimum width of the hearth should be a minimum of 6 feet (4 feet + 1 foot on each side).

In addition to width, the hearth must also extend outward in front of the firebox, typically a minimum distance of 16 inches but can vary based on the specific fireplace design and code requirements. Given the choices, a hearth dimension of 6 feet wide and 20 inches out provides an adequate safety margin both in width and depth, complying with the general requirements to extend well beyond the firebox dimensions. Thus, it aligns with the standards for hearth sizes, ensuring proper coverage and safety measures.