Option D is correct because 'despite' is never followed by 'of' - it stands alone. Options A, B, and C are grammatically incorrect: 'Despite of' (A) should be just 'despite'; 'inspite of' (B) should be 'in spite of' (two words); 'in spite my being' (C) should be 'in spite of my being'. The rule is: use 'despite' alone or 'in spite of' (three words with 'of').