To obtain data from a specific equation in Mathematica for plotting in MATLAB using the imagesc command, the process involves defining the function and generating a data table over the desired variable range. For example, the function F[x, y] = Sin[x 5] Sin[y 5] can be used, and a data table can be created with the command Table[F[x, y], {x, 0, 1, 0.1}, {y, 0, 1, 0.1}]. This data can then be visualized in Mathematica using ListPlot3D. To transfer the data to MATLAB, it should be exported as a MATLAB matrix file using Export["c://data.MAT", data], allowing for easy import into MATLAB for further plotting with imagesc.