Answer
$4a$
Work Step by Step
When a grouping symbol is preceeded by a minus sign, removing the grouping symbol implies reversing the sign of all the terms inside the grouping symbol. Hence, the given expression, $
a-\{3a-[4a-(2a-4a)]\}
,$ is equivalent to
\begin{array}{l}\require{cancel}
a-\{3a-[4a-(2a-4a)]\}
\\\\=
a-\{3a-[4a-2a+4a]\}
\\\\=
a-\{3a-4a+2a-4a\}
\\\\=
a-3a+4a-2a+4a
.\end{array}
Carrying the subtraction and addition operators from left to right, the expression above simplifies to
\begin{array}{l}\require{cancel}
a-3a+4a-2a+4a
\\\\=
-2a+4a-2a+4a
\\\\=
2a-2a+4a
\\\\=
0+4a
\\\\=
4a
.\end{array}
