Explanation:

Let’s decode the pattern step by step:

- Look at HECK (coded as 94410):

- H(8), E(5), C(3), K(11) as per alphabetical order.

- If you take each letter's position and square it:

- H: 8² = 64

- E: 5² = 25

- C: 3² = 9

- K: 11² = 121

- Arrange: 64, 25, 9, 121 ? Not matching 94410.

- Try concatenating instead: H(8) E(5) C(3) K(11) ? 85311? No match.

- Now, reverse the letters' positions: K(11) C(3) E(5) H(8) = 11358. No match.

- Let's check for the digits: HECK = 9 4 4 10 (does H=9, E=4, C=4, K=10 correspond to alphabet? But H is the 8th, not 9th.)

- Seems they assigned digit values (example: H=9, E=4, C=4, K=10).

- Now look at DIG (coded as 588):

- D: 4, I: 9, G: 7

- Code given is 588.

- Try adding 1 to each letter's position: D(4)+1=5, I(9)-1=8, G(7)+1=8 ? 5 8 8.

- Pattern: alternate +1, -1, +1.

Let’s apply this to BIKE:

- B (2), I (9), K (11), E (5)

- Use the pattern: +1, -1, +1, -1

- B: 2+1 = 3

- I: 9-1 = 8

- K: 11+1 = 12

- E: 5-1 = 4

- Combined: 3 8 12 4

Check the options:

1. 38124

2. 19113

3. 38115

4. 39105

So, the correct coding is Option: 1, 38124.

Key points explained:

- The code pattern alternates between adding and subtracting 1 from each letter’s alphabetical order.

- HECK = 94410 because H(8)+1=9, E(5)-1=4, C(3)+1=4, K(11)-1=10.

- DIG = 588 follows the same pattern.

- BIKE, by pattern, is coded as 38124.