Find the matrix $A$ such that the following is true:$ T_1(T_2(\mathbf{x})) = A\mathbf{x}$?
look at what $$T_1\left(T_2\pmatrix{1\\0}\right) = T_1\pmatrix{-2\\0} =\pmatrix{-6\\4} \tag 1$$ i will let you work through $$T_1\left(T_2\pmatrix{0\\1}\right)= \pmatrix{a\\b}\tag2 $$
once you have $(1)$ and $(2),$ you can write $$T_1\left(T_2\pmatrix{x_1\\x_2}\right) = \pmatrix{-6x_1+ax_2\\4x_1+bx_2}=A\pmatrix{x_1\\x_2}$$ where $$A=\pmatrix{-6&a\\4&b}.$$