\[a_{4} = 6;\ \ \ a_{6} = 1,2.\]
\[a_{4} = a_{1} + 3d = 6 \rightarrow a_{1} = 6 - 3d;\]
\[a_{6} = a_{1} + 5d = 1,2 \rightarrow a_{1} = 1,2 - 5d.\]
\[6 - 3d = 1,2 - 5d\]
\[- 3d + 5d = 1,2 - 6\]
\[2d = - 4,8\]
\[d = - 2,4.\]
\[a_{1} = 1,2 - 5d = 1,2 - 5 \cdot ( - 2,4) =\]
\[= 1,2 + 12 = 13,2.\]
\[a_{11} = a_{1} + 10d = 13,2 + 10 \cdot ( - 2,4) =\]
\[= 13,2 - 24 = - 10,8.\]
\[S_{11} = \frac{\left( a_{1} + a_{11} \right) \cdot 11}{2} = \frac{(13,2 - 10,8) \cdot 11}{2} =\]
\[= \frac{2,4 \cdot 11}{2} = 1,2 \cdot 11 = 13,2.\]
\[Ответ:13,2.\]