Which two numbers and two signs should be interchanged in the following equation to make it correct?

$$7 \times 14 \div 6 + 12 + 6 = 30$$

The given (incorrect) equation is $$7 \times 14 \div 6 + 12 + 6 = 30$$.

We must interchange exactly two numbers and exactly two signs so that the left-hand side evaluates to $$30$$, following the BODMAS (PEMDAS) order.

Case 1: Option A
Interchange the numbers $$7$$ and $$6$$ and the signs $$\times$$ and $$\div$$.
Equation becomes: $$6 \div 14 \times 7 + 12 + 7$$.
Evaluate: $$6 \div 14 = \frac{3}{7}$$, $$\frac{3}{7} \times 7 = 3$$, sum $$3 + 12 + 7 = 22 \neq 30$$.
Hence Option A is wrong.

Case 2: Option B
Interchange the numbers $$7$$ and $$14$$ and also interchange the signs $$\times$$ and $$\div$$.
Original order of terms and signs: $$7\,(\times)\,14\,(\div)\,6$$.
After swapping numbers: $$14\,(\times)\,7\,(\div)\,6$$.
After swapping signs: replace each $$\times$$ with $$\div$$ and each $$\div$$ with $$\times$$.
Thus the new equation is
$$14 \div 7 \times 6 + 12 + 6 = ?$$

Now calculate step by step:
$$14 \div 7 = 2$$,
$$2 \times 6 = 12$$.
Add the remaining terms: $$12 + 12 + 6 = 30$$.

The left-hand side now equals the right-hand side, so the equation is correct. Therefore Option B satisfies the requirement.

Case 3: Option C
Interchange the numbers $$7$$ and $$6$$ and the signs $$\div$$ and $$+$$.
New equation: $$6 \times 14 + 7 \div 12 \div 6$$ (after performing both swaps).
Even a quick estimate shows the product $$6 \times 14 = 84$$ already exceeds $$30$$, so Option C is impossible.

Case 4: Option D
Interchange the numbers $$7$$ and $$14$$ and the signs $$\times$$ and $$+$$.
New equation: $$14 + 7 \div 6 \times 12 \times 6$$.
Again, the presence of two multiplications makes the value far larger than $$30$$, so Option D is wrong.

Hence the only choice that makes the equation correct is

Option B which is: 7 and 14, $$\times$$ and $$\div$$.