Answer
$counter\,\,example\,\,:\\
A=\left \{5,6 \right \},B=\left \{ 6,7 \right \},C=\left \{ 5,8 \right \}$
Work Step by Step
$For\,\,all\,\,sets\,\,A,\,B,\,and\,\,C\,\\
(A \cap B) \cup C = A \cap (B \cup C).\\
this\,\,not\,\,true:\\
counter\,\,example\,\,:\\
A=\left \{5,6 \right \},B=\left \{ 6,7 \right \},C=\left \{ 5,8 \right \}\\
A \cap B=\left \{5,6 \right \}\cap \left \{ 6,7 \right \}=\left \{ 6 \right \}\\
(A \cap B) \cup C=\left \{ 6 \right \}\cup \left \{ 5,8 \right \}=\left \{ 5,6,8 \right \} {\color{Red} (1)}\\
B\cup C=\left \{ 5,6,7,8 \right \}\\
A \cap (B \cup C)=\left \{ 5,6 \right \}\cap \left \{ 5,6,7,8 \right \}=\left \{ 5,6 \right \}{\color{Red} (2)} \\
from\,\,1,2\,\,(A \cap B) \cup C =\left \{ 5,6,8 \right \}\neq \left \{ 5,6 \right \}= A \cap (B \cup C)$