How do you evaluate $2\left[ 3\left( 7-5 \right)+4\left( 8+2 \right) \right]$?

Hint: Assume the given expression as ‘E’. Now, first simplify the terms inside the small bracket by performing simple addition or subtraction, whichever required. Now, in the next step consider the respective products and simplify the terms inside the square bracket. Finally multiply the obtained sum with 2 that is present outside the square bracket to get the answer.

Complete step-by-step answer:
Here, we have been provided with the expression $2\left[ 3\left( 7-5 \right)+4\left( 8+2 \right) \right]$ and we are asked to evaluate it. That means we have to find the numerical value that will be obtained by simplifying the expression.
Now, let us assume the value of the given expression as E. So, we have,
$\Rightarrow E=2\left[ 3\left( 7-5 \right)+4\left( 8+2 \right) \right]$
Now, we need to simplify the terms inside the small bracket first, according to the BODMAS rule. So, simplifying the terms inside the small bracket, we get,
$\Rightarrow E=2\left[ 3\left( 2 \right)+4\left( 10 \right) \right]$
Now, multiplying 3 with 2 and 4 with 10 inside the square bracket, we get,
$\Rightarrow E=2\left[ 6+40 \right]$
Now, simplifying the terms inside the square bracket, we get,
$\Rightarrow E=2\left[ 46 \right]$
Multiplying 2 with 46 we get,
$\Rightarrow E=92$
Hence, the value of the given expression is 92 which is our answer.

Note: One may note that we have applied the BODMAS rule to simplify the expression. Although it is not necessary to use it as we can get the answer by using the distributive property of multiplication also. But if we do so, the expression will become lengthy and we would require some calculations to perform. This problem is resolved using the BODMAS rule as it performs the operations systematically.