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4)none of these

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For an m×n chessboard there are 2m+2n−2 ways.

Case I. There are two horizontally adjacent squares of the same color: 2m−2 ways.

Case II. There are two vertically adjacent squares of the same color: 2n−2 ways.

Case III. None of the above: 2 ways.

Hint for Case I: There are 2m−2 ways to color one row so that two adjacent squares have the same color. 

The rest of the coloring is determined from that; colors must alternate in each column. (Note, therefore, that Cases I and II do not overlap.)

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