Factorize each of the following algebraic expressions:

$-4(x-2 y)^{2}+8(x-2 y)$

$=[-4(x-2 y)+8](x-2 y) \quad[$ Taking $(x-2 y)$ as the common factor $]$

$=4[-(x-2 y)+2](x-2 y) \quad\{$ Taking 4 as the common factor of $[-4(x-2 y)+8]\}$

$=4(2 y-x+2)(x-2 y)$