Simplify :
`2{m - 3(n + bar(m- 2n))}`

Answer

To simplify the expression \( 2(m - 3(n + \overline{m - 2n})) \), we will follow a systematic approach.

### Step 1: Simplify the inner expression
First, we need to simplify the expression inside the bar. The expression is \( m - 2n \).

### Step 2: Apply the bar notation
The bar notation indicates that we need to consider the negation of the expression. Therefore, \( \overline{m - 2n} = - (m - 2n) = -m + 2n \).

### Step 3: Substitute back into the expression
Now, substitute this back into the original expression:
\[ 2(m - 3(n + \overline{m - 2n})) = 2(m - 3(n + (-m + 2n))) \]
This simplifies to:
\[ 2(m - 3(n - m + 2n)) \]

### Step 4: Combine like terms
Now, simplify the expression inside the parentheses:
\[ n - m + 2n = 3n - m \]
So the expression becomes:
\[ 2(m - 3(3n - m)) \]

### Step 5: Distribute the -3
Next, distribute the \(-3\):
\[ 2(m - 9n + 3m) = 2(4m - 9n) \]

### Step 6: Multiply by 2
Now, multiply the entire expression by 2:
\[ 2(4m - 9n) = 8m - 18n \]

### Final Result
Thus, the simplified expression is:
\[ 8m - 18n \]

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