With engineering shear strain γxy, plane compatibility is $\partial^2\epsilon_{xx}/\partial y^2+\partial^2\epsilon_{yy}/\partial x^2=\partial^2\gamma_{xy}/(\partial x\partial y)$. The left side is 2A+2A and the right side B. Hence B = 4A, D. Using tensor shear strain instead would introduce a factor of two, which is why the γ notation matters.
More Special topics: Equilibrium and compatibility equations in two-dimensional elasticity questions
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