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Not enough information is given. We are only given two of the board's dimensions, and you haven't specified which dimensions those are. Presumably you mean thickness and width.

Even with that, we would still need to know ~at least~ the length of the board and what material it is (pine? maple? something else altogether?). Even then, the answer could only be a very rough one, as there are many other factors that would need to be specified or guessed (the moisture of the wood, the positioning of the weight on the board, how the board is supported, the temperature, and so on).

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Q: How much weight does it take to break a 2 x 6 board?
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