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2 dimensions is having only the dimensions of height and width, like a square. 3 dimensions is having height, width and depth, like a cube.
It is possible you are referring to length, width and height (or depth). If you mean the values then there is an infinite number of them
A circle is two dimensional because the two dimensions are width and length. 3 dimensional would be width, length and depth but since you can just write it on paper, it has no depth.
A plane has two dimensions, length and width.
In 2 dimensions, a quadrilateral. In 3 dimensions, a tetrahedron.