Corners are cut off from an equilateral triangle T to produce a regular hexagon H. Then, the ratio of the area of H to the area of T is

Let the side length of the equilateral triangle T be $3a$. To form a regular hexagon H by cutting off the three corners, each corner cut off must be an equilateral triangle of side length $a$.

This division splits the original equilateral triangle T into 9 identical small equilateral triangles, each of side length $a$.

The three cut-off corner triangles account for $3$ of these small triangles, leaving the regular hexagon H to consist of the remaining:
$9-3=6$ small equilateral triangles.

Therefore, the ratio of the area of the regular hexagon H to the area of the equilateral triangle T is:
$\frac{\text{Area of H}}{\text{Area of T}}$

Thus, the ratio is 2: 3. The correct option is 4.