In the number “847291536”, if each even digit is increased by 1 and each odd digit is decreased by 1, and then the resulting digits are arranged in ascending order from left to right, what will be the product of the digit that is fourth from the left end and the digit that is third from the right end?

The correct answer is 28.

Step 1: Understand the given number and rules

The original given number is 847291536.
We need to modify each digit based on whether it is even or odd:

• If a digit is even, increase it by 1 (+1).
• If a digit is odd, decrease it by 1 (-1).

Step 2: Apply the modifications digit by digit

Processing each digit from left to right:

• Digit 8 (even): $8+1=9$

• Digit 4 (even): $4+1=5$

• Digit 7 (odd): $7-1=6$

• Digit 2 (even): $2+1=3$

• Digit 9 (odd): $9-1=8$

• Digit 1 (odd): $1-1=0$

• Digit 5 (odd): $5-1=4$

• Digit 3 (odd): $3-1=2$

• Digit 6 (even): $6+1=7$

The resulting sequence of modified digits is: 9, 5, 6, 3, 8, 0, 4, 2, 7.

Step 3: Arrange the modified digits in ascending order

Arranging these digits from left to right in ascending order (smallest to largest):
0, 2, 3, 4, 5, 6, 7, 8, 9

Step 4: Identify the required positions and calculate the product

1. The digit that is fourth from the left end is 4.
(Positions from left: 1st = 0, 2nd = 2, 3rd = 3, 4th = 4)

2. The digit that is third from the right end is 7.
(Positions from right: 1st = 9, 2nd = 8, 3rd = 7)

3. Calculate the product of these two digits:

$4\times 7=28$

Therefore, the product of the fourth digit from the left end and the third digit from the right end is 28.