Mapping square objects to specific cells in a TableLayoutPanel in WindowsForms game
The problem of your code is that you use separate conditions for each particular row and for each particular column.
But it can be easily aggregated into one - check if the row number is odd. A rest of the desired functionality can be reached using arithmetics.  

Please try this code:

private static void MapSquareNumToScreenRowAndColumn(int squareNumber, out int rowNumber, out int columnNumber)
{
    const int Rows = 7;
    const int Cols = 6;

    // Calculate the rowNumber and the columnNumber at once.
    // See Math.DivRem for details: http://msdn.microsoft.com/en-us/library/yda5c8dx(v=vs.110).aspx
    rowNumber = Rows - 1 - Math.DivRem(squareNumber, Cols, out columnNumber);

    // If the rowNumber is odd:
    if ((rowNumber &amp; 1) != 0)  // (rowNumber &amp; 1) is the same as (rowNumber % 2)
        columnNumber = Cols - 1 - columnNumber;  // Invert the columnNumber
}