To evaluate the expression \(4_2 + (3 \times 6) - 7\), we first need to convert \(4_2\) (which is in base 2) to decimal.
In base 2:
- \(4_2\) is not a valid representation because \(4\) is not a digit in base 2. The valid digits in base 2 are \(0\) and \(1\). Therefore, it seems there might be a misunderstanding or an error in the base notation.
If you intended to write a decimal \(4\) instead of \(4_2\), let's evaluate as follows:
- \(4 + (3 \times 6) - 7\)
Calculate \(3 \times 6\): \[ 3 \times 6 = 18 \]
Now substitute back into the expression: \[ 4 + 18 - 7 \]
Now solve the addition: \[ 4 + 18 = 22 \]
Finally, subtract \(7\): \[ 22 - 7 = 15 \]
Thus, the evaluated expression is: \[ \boxed{15} \]
If you were actually asking about a different base or a specific calculation method, please clarify!