Answer
$6$
Work Step by Step
The given expression, $
2-[10-(5+12\div2^2\cdot3)]
,$ simplifies to
\begin{array}{l}
2-[10-(5+12\div4\cdot3)]
\\\\=
2-[10-(5+3\cdot3)]
\\\\=
2-[10-(5+9)]
\\\\=
2-[10-14]
\\\\=
2-[-4]
\\\\=
2+4
\\\\=
6
.\end{array}