Answer
$For\,\,all\,\,sets\,\,A,\,B,\,\,and\,C\,\,\\
if\,\,A \subseteq B\,then\,\,A \cap (B \cap C)^c = \varnothing \\
this\,\,is\,\,false:\\
counter\,\,example\,\,:\\
U=\left \{ 6,7,8,9 \right \}\\
A=\left \{ 6,7 \right \},B=\left \{ 6,7,8 \right \},C=\left \{ 8,9 \right \}\\
A\subseteq B\,\,\,(\left \{ 6,7 \right \}\subseteq \left \{ 6,7,8 \right \})\\
B\cap C=\left \{ 6,7,8 \right \}\cap \left \{ 8,9 \right \}=\left \{ 8 \right \}\\
(B\cap C)^c=\left \{ 6,7,9 \right \}\\
A \cap (B \cap C)^c=\left \{ 6,7 \right \}\cap \left \{ 6,7,9 \right \}=\left \{ 6,7 \right \}\\
\therefore A \cap (B \cap C)^c\neq \varnothing
$
Work Step by Step
$For\,\,all\,\,sets\,\,A,\,B,\,\,and\,C\,\,\\
if\,\,A \subseteq B\,then\,\,A \cap (B \cap C)^c = \varnothing \\
this\,\,is\,\,not\,\,true:\\
counter\,\,example\,\,:\\
U=\left \{ 6,7,8,9 \right \}\\
A=\left \{ 6,7 \right \},B=\left \{ 6,7,8 \right \},C=\left \{ 8,9 \right \}\\
A\subseteq B\,\,\,(\left \{ 6,7 \right \}\subseteq \left \{ 6,7,8 \right \})\\
B\cap C=\left \{ 6,7,8 \right \}\cap \left \{ 8,9 \right \}=\left \{ 8 \right \}\\
(B\cap C)^c=\left \{ 6,7,9 \right \}\\
A \cap (B \cap C)^c=\left \{ 6,7 \right \}\cap \left \{ 6,7,9 \right \}=\left \{ 6,7 \right \}\\
\therefore A \cap (B \cap C)^c\neq \varnothing
$
