$ t_1 + t_2 + t_3 = -24 \Rightarrow t_1 + t_1q + t_1q^2 = -24 \Rightarrow t_1(1+q+q^2)=-24 \\ t_1 + t_2 + ... + t_6=-21 \Rightarrow t_1(1+q+q^2+q^3+q^4+q^5)=-21 \\ t_1(1+q+q^2) +q^3t_1(1+q+q^2) = -21 \\ \Rightarrow -24 + q^3(-24) = -21 \\ -24q^3=  3 \Rightarrow q^3 = \frac{-1}{8} \\ \frac{t_4}{t_{10}}=\frac{t_1q^3}{t_1q^9} = \frac{1}{q^6} = \frac{1}{(\frac{-1}{8})^2} = 64  $