Simplify :
`2[6 + 4{m - 6(7-bar(n+p)) + q}]`

Answer

To simplify the expression \( 2[6 + 4(m - 6(7 - \bar{(n + p)}) + q)] \), we will follow the order of operations (BODMAS/BIDMAS). Here’s the step-by-step solution:

### Step 1: Simplify the innermost expression
Start with the innermost part of the expression, which is \( 7 - \bar{(n + p)} \). The bar notation indicates negation, so we can rewrite it as:
\[ 7 - (n + p) = 7 - n - p \]

### Step 2: Substitute back into the expression
Now, substitute this back into the expression:
\[ 2[6 + 4(m - 6(7 - n - p) + q)] \]

### Step 3: Distribute the -6
Next, we need to distribute the -6 across the terms inside the parentheses:
\[ m - 6(7 - n - p) + q = m - 42 + 6n + 6p + q \]

### Step 4: Substitute back again
Now substitute this back into the expression:
\[ 2[6 + 4(m - 42 + 6n + 6p + q)] \]

### Step 5: Distribute the 4
Now, distribute the 4:
\[ 4(m - 42 + 6n + 6p + q) = 4m - 168 + 24n + 24p + 4q \]

### Step 6: Combine with the outer expression
Now combine this with the 6 from the outer expression:
\[ 6 + 4m - 168 + 24n + 24p + 4q = 4m + 24n + 24p + 4q - 162 \]

### Step 7: Multiply by 2
Now multiply the entire expression by 2:
\[ 2(4m + 24n + 24p + 4q - 162) = 8m + 48n + 48p + 8q - 324 \]

### Final Result
Thus, the simplified expression is:
\[ 8m + 48n + 48p + 8q - 324 \]

---