The value of question mark is
 \[\left( {\begin{array}{*{20}{c}}
  5&4&7 \\
  {12}&6&6 \\
  7&?&2
\end{array}} \right)\]

Hint: Missing number are the number that got missed in the given series of number similar differences among them. The process of writing the missing numbers is termed as finding similar changes between those number are filling their missing values in their specific series and places

Complete answer:
Given table is:
\[\left( {\begin{array}{*{20}{c}}
  5&4&7 \\
  {12}&6&6 \\
  7&?&2
\end{array}} \right)\]
To find?
Now in this question as the numbers are given in the square form which contain row and Coolum. Here
Let \[{a_1},{a_2},{a_3}\] for number in ROW I
\[{a_4},{a_5},{a_6}\] for ROW II
\[{a_7},{a_8},{a_9}\] for ROW III
Now applying the logic
We can see that
When
\[{a_1} + {a_3} = \]sum of number in Colum I & III of Row I
i.e. \[5 + 7 = 12\] which is clearly divisible by \[3\]
clearly quotient \[ = 4\]
where \[4\] is that number which is in middle Row i.e. \[{a_2} = 4\]
Similarly for Row II
\[{a_4} + {a_6} \Rightarrow 12 + 6 = 18\]
Which is clearly divisible\[3\]
Quotient \[ = 6\]
Which is middle term of Row II
i.e. \[{a_5} = 6\]
Now applying the same logic for Row III, to find? i.e. to find as adding
\[{a_7} + {a_9} \Rightarrow 7 + 2 = 9\]
Which is clearly divisible by \[9\]
Quotient \[ = 3\]
It should be a middle term of Row III i.e.
\[? = {a_8} = 3\]

Note: Generally these types of problems are mostly based on logical thinking.To find the missing number first we have to find the logic behind other given numbers.If we observe the second and third rows were copied down, unchanged, into the second matrix. We use the basic logic to resolve the problem.