You probably should reread the specifications. “Check if the first dimensions and the second dimensions of each 2-dim. array array are the same” means that you should check if first and second matrix lengths match; it does not mean to test doubMatrix1[i][j] == doubMatrix2[i][j]. If Also test sizes of doubMatrix1[0] and doubMatrix2[0]; ie besides testing doubMatrix1.length vs doubMatrix2.length, test doubMatrix1[0].length vs doubMatrix2[0].length. If the sizes don't match, then do your return tempArray = new double[0][0]; statement, or perhaps return new double[0][0];. That particular statement should be before, not inside, the nested for loops.
“Add each corresponding element in the parameter 2-dim. arrays and store the result” means to do something like your
tempArray[i][j] = doubMatrix1[i][j] + doubMatrix2[i][j];
statement. However, your code repeatedly reallocates tempArray[][], so tempArray[][] never has more than one element set in it. Allocate the array earlier in your program, perhaps after you know the sizes match.