The question is asking for the number of identical small equilateral triangular plates that a given equilateral triangular plate can be cut into.

Option 1 suggests 196 cuttings. However, 196 cannot represent the number of identical small equilateral triangles because it`s not a power of 4. An equilateral triangle can only be divided into 4, 16, 64 and so on, which are the power of 4.

Option 2 suggests 216 cuttings. Again, 216 cannot represent the number of identical small triangles because it`s not a power of 4, but it`s a power of 6 (6^3).

Option 3 suggests 256 cuttings. This is the correct answer because 256 is a power of 4 (4^4). Thus, an equilateral triangle can indeed be divided into 256 identical smaller equilateral triangles.

Option 4 suggests 296 cuttings. But, like the previous options, 296 can’t represent the number of identical small equilateral triangles as it`s not a power of 4.

So, the correct answer is 256 as given in option 3.