To solve the equation `2 + 4 - 6 x 4 = 10` by finding the correct order of operations, we will evaluate each option provided to see which one makes the equation true.
### Step-by-Step Solution:
1. **Identify the Original Equation**:
The original equation is:
\[
2 + 4 - 6 \times 4 = 10
\]
2. **Evaluate the Left-Hand Side (LHS)**:
According to the order of operations (PEMDAS/BODMAS), we perform multiplication before addition and subtraction:
\[
LHS = 2 + 4 - (6 \times 4)
\]
Calculate \(6 \times 4\):
\[
6 \times 4 = 24
\]
Now substitute back:
\[
LHS = 2 + 4 - 24
\]
Calculate \(2 + 4\):
\[
2 + 4 = 6
\]
Now substitute:
\[
LHS = 6 - 24 = -18
\]
Since \(-18 \neq 10\), the original equation is incorrect.
3. **Check Each Option**:
We will check each option provided to find the correct order of operations.
**Option 1**: Multiply, Add, Subtract, Equals
\[
2 \times 4 + 6 - 10
\]
Calculate:
\[
2 \times 4 = 8
\]
Substitute:
\[
8 + 6 - 10 = 4 \quad (\text{not equal to } 10)
\]
**Option 2**: Subtract, Multiply, Equals, Add
\[
2 - 4 \times 6 = 4 + 10
\]
Calculate:
\[
4 \times 6 = 24
\]
Substitute:
\[
2 - 24 = 4 + 10 \Rightarrow -22 = 14 \quad (\text{not equal to } 10)
\]
**Option 3**: Equals, Subtract, Multiply, Add
\[
2 = 4 - 6 \times 4 + 10
\]
Calculate:
\[
6 \times 4 = 24
\]
Substitute:
\[
2 = 4 - 24 + 10
\]
Calculate:
\[
4 - 24 = -20 \quad \Rightarrow -20 + 10 = -10 \quad (\text{not equal to } 10)
\]
**Option 4**: Subtract, Equals, Add, Multiply
\[
2 - 4 = 6 + 4 \times 10
\]
Calculate:
\[
4 \times 10 = 40
\]
Substitute:
\[
2 - 4 = 6 + 40
\]
Calculate:
\[
-2 = 46 \quad (\text{not equal to } 10)
\]
**Option 5**: Multiply, Add, Subtract, Equals
\[
2 \times 4 + 6 - 10
\]
Calculate:
\[
2 \times 4 = 8
\]
Substitute:
\[
8 + 6 - 10 = 4 \quad (\text{not equal to } 10)
\]
4. **Final Evaluation**:
After evaluating all options, we find that none of the options provided yield a correct equation that equals 10.
### Conclusion:
The correct order of operations that makes the equation valid is not present in the options provided.
