$$10 - 5 \times 10 - 8 \times 10 6 \times ( - 1 ) 3 10 - 4 \times ( - 1 ) 8$$
$$\textbf{Step 1: Solving Multiplications first.}$$
$$10-5\times10-8\times106\times(-1)310-4\times(-1)8$$$$=10-{5×10}-{8×106×(-1)×310}-{4×(-1)×8}$$
$$=10-50-(-262880)-(-32)$$
$$\textbf{Step 2: Resolving signs.}$$
$$10 - 5 \times 10 - 8 \times 10 6 \times ( - 1 ) 3 10 - 4 \times ( - 1 ) 8$$$$= 10-50-(-262880)-(-32)$$
$$=10-50+262880+32$$ $$\mathbf{[\because (-)×(-)=(+)]}$$
$$\textbf{Step 3: Solving the expression from left to right.}$$
$$10 - 5 \times 10 - 8 \times 10 6 \times ( - 1 ) 3 10 - 4 \times ( - 1 ) 8$$$$=-40+262880+32$$
$$=262840+32$$
$$=262872$$
$$\textbf{Hence, }\mathbf{10-5×10-8×106×\left(-1\right)310-4×\left(-1\right)8 = 262872}$$