Which two signs/numbers need to be interchanged to make the given equation correct?

8 ÷ 2 + 4 = 10

The correct option is + and ÷, 2 and 4.

To understand why this is the correct choice, let us analyze the given mathematical equation step-by-step.

The original equation is:

$8÷2+4=10$

According to the BODMAS rule, division must be performed before addition. Let us evaluate the left-hand side (LHS) of the original equation:
First, calculate the division:
$8÷2=4$
Next, add 4 to the result:
$4+4=8$
Since $8\ne 10$, the original equation is incorrect.

Now, let us interchange the signs + and ÷, and the numbers 2 and 4 in the original equation:
1. Swap the division sign (÷) and the addition sign (+).
2. Swap the numbers 2 and 4.

Applying these interchanges to the original expression $8÷2+4$ gives:
- The first operator (÷) becomes (+).
- The second operator (+) becomes (÷).
- The number 2 becomes 4.
- The number 4 becomes 2.

This results in the new LHS expression:

$8+4÷2$

Let us evaluate this new expression using the order of operations (division first):
First, perform the division:
$4÷2=2$
Next, perform the addition:
$8+2=10$

The evaluated LHS is now equal to the right-hand side (10). Thus, interchanging + and ÷ along with the numbers 2 and 4 makes the equation correct.