Correct choice is (c) 3×8

The best I can explain: For plane elasticity problems the strain-displacement relation is given by ε=BD, where ε=[εxxεyyεxy]^T, B=\(\begin{pmatrix}\frac{\partial \psi_1}{\partial x}&0&\frac{\partial \psi_2}{\partial y}&0&…&\frac{\partial \psi_n}{\partial y}&0\\0&\frac{\partial \psi_1}{\partial y}&0&\frac{\partial \psi_2}{\partial y}&…&0&\frac{\partial \psi_n}{\partial y}\\\frac{\partial \psi_1}{\partial y}&\frac{\partial \psi_1}{\partial x}&\frac{\partial \psi_2}{\partial y}&\frac{\partial \psi_2}{\partial x}&…&\frac{\partial \psi_n}{\partial y}&\frac{\partial \psi_n}{\partial x}\end{pmatrix}\) and D=\(\begin{bmatrix}u_x^1&u_y^1&u_x^2&u_y^2&u_x^3&u_y^3\end{bmatrix}\)^T. The order of matrix B is 3x2n, where n is the number of nodes in the element. A linear quadrilateral element has four nodes, thus n=4.

Order of B is 3×2*4

=3×8.