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Using the eldo's data:

m = Partition[Range @ 100, 10]; 

An alternative is to use TakeDrop:

dropRC[m_, rows : {_, _}, cols : {_, _}] := TakeDrop[ Transpose@TakeDrop[Transpose@m, rows][[2]], cols][[2]]; dropRC[m, {2, 6}, {2, 3}] // MatrixForm