At least six heads.

P(At least six heads) = P(X>=6)

P(X>=6) = P(X=6) + P(X=7) + P(X=8) + P(X=9) + P(X=10)

              =  ¹⁰C₆(1/2)¹⁰ + ¹⁰C₇(1/2)¹⁰ + ¹⁰C₈(1/2)¹⁰ + ¹⁰C₉(1/2)¹⁰ + ¹⁰C₁₀(1/2)¹⁰ 

              = 193/512