What will come in place of question mark (?) in the following questions ?
`(6-sqrt(?)) - (2(6-sqrt(?)))/(3^(2) - (sqrt(?))^(2)) = 3(6-sqrt(?))`

Options

A. 10
B. 6
C. 2
D. 3

Answer

To solve the equation

\[ (6 - \sqrt{?}) - \frac{2(6 - \sqrt{?})}{3^2 - (\sqrt{?})^2} = 3(6 - \sqrt{?}), \]

we will follow these steps:

### Step 1: Rewrite the equation
We start by rewriting the equation for clarity:

\[ (6 - \sqrt{?}) - \frac{2(6 - \sqrt{?})}{9 - ?} = 3(6 - \sqrt{?}). \]

### Step 2: Factor out the common term
Next, we can factor out \( (6 - \sqrt{?}) \) from the left-hand side:

\[ (6 - \sqrt{?}) \left( 1 - \frac{2}{9 - ?} \right) = 3(6 - \sqrt{?}). \]

### Step 3: Cancel the common term
Assuming \( 6 - \sqrt{?} \neq 0 \), we can safely divide both sides by \( (6 - \sqrt{?}) \):

\[ 1 - \frac{2}{9 - ?} = 3. \]

### Step 4: Isolate the fraction
Now, we isolate the fraction:

\[ -\frac{2}{9 - ?} = 3 - 1, \]
which simplifies to:

\[ -\frac{2}{9 - ?} = 2. \]

### Step 5: Remove the negative sign
Multiplying both sides by -1 gives:

\[ \frac{2}{9 - ?} = -2. \]

### Step 6: Cross-multiply
Cross-multiplying yields:

\[ 2 = -2(9 - ?). \]

### Step 7: Distribute and simplify
Distributing the -2 gives:

\[ 2 = -18 + 2?. \]

### Step 8: Rearranging the equation
Rearranging the equation to isolate terms involving \( ? \):

\[ 2? = 2 + 18, \]
which simplifies to:

\[ 2? = 20. \]

### Step 9: Solve for ?
Dividing both sides by 2 gives:

\[ ? = 10. \]

### Final Answer
Thus, the value that comes in place of the question mark is:

\[ \boxed{10}. \]