In each of the following questions, an equation becomes incorrect due to the interchange of two signs. One of the four alternatives under it specifies the interchange of signs in the equation, which when made will make the equation correct. Find the correct alternative.
`12-:2-6 xx 3 + 8 = 16`

Options

A. `-:` and +
B. `-` and +
C. ` xx` and +
D. `-:` and ` xx `

Explanation

To solve the equation \( 12 -: 2 - 6 \times 3 + 8 = 16 \) and find the correct alternative by interchanging two signs, we will follow these steps:

### Step 1: Understand the Given Equation
The equation is:
\[ 12 -: 2 - 6 \times 3 + 8 = 16 \]
Here, the signs are incorrect due to the interchange of two signs.

### Step 2: Identify Possible Interchanges
We need to check the options provided to see which two signs can be interchanged to make the equation correct. The possible operations are division, multiplication, addition, and subtraction.

### Step 3: Evaluate the Options
Let's evaluate the options one by one.

#### Option 1: Interchange Division with Addition
If we interchange the division ( -: ) with addition (+):
\[ 12 + 2 - 6 \times 3 - 8 \]
Now, we will solve this step by step:
1. Perform the multiplication first:
\[ 6 \times 3 = 18 \]
2. Substitute back into the equation:
\[ 12 + 2 - 18 - 8 \]
3. Now, perform the addition and subtraction from left to right:
\[ 14 - 18 - 8 = -4 - 8 = -12 \quad (\text{not equal to } 16) \]

#### Option 2: Interchange Minus with Plus
If we interchange minus (-) with plus (+):
\[ 12 -: 2 + 6 \times 3 - 8 \]
Now, we will solve this step by step:
1. Perform the division first:
\[ 12 -: 2 = 6 \]
2. Substitute back into the equation:
\[ 6 + 6 \times 3 - 8 \]
3. Perform the multiplication:
\[ 6 \times 3 = 18 \]
4. Substitute back:
\[ 6 + 18 - 8 \]
5. Now, perform the addition and subtraction:
\[ 24 - 8 = 16 \quad (\text{equal to } 16) \]

#### Option 3: Interchange Division with Multiplication
If we interchange division (-:) with multiplication (×):
\[ 12 \times 2 - 6 - 8 \]
1. Perform the multiplication:
\[ 12 \times 2 = 24 \]
2. Substitute back:
\[ 24 - 6 - 8 \]
3. Perform the subtraction:
\[ 24 - 6 = 18 \]
\[ 18 - 8 = 10 \quad (\text{not equal to } 16) \]

#### Option 4: Interchange Minus with Division
If we interchange minus (-) with division (-:):
\[ 12 - 2 - 6 \times 3 + 8 \]
1. Perform the subtraction:
\[ 12 - 2 = 10 \]
2. Substitute back:
\[ 10 - 6 \times 3 + 8 \]
3. Perform the multiplication:
\[ 6 \times 3 = 18 \]
4. Substitute back:
\[ 10 - 18 + 8 \]
5. Perform the subtraction and addition:
\[ -8 + 8 = 0 \quad (\text{not equal to } 16) \]

### Conclusion
The only option that makes the equation correct is **Option 2**, where we interchange minus with plus.