This question asks us to find the coding pattern used for the word 'PUSH' and then apply the same pattern to find the code for the word 'HIKE'.

Decoding the Pattern for 'PUSH'

First, let's list the letters in the word PUSH and their corresponding positions in the English alphabet:

• P is the 16^th letter.
• U is the 21^st letter.
• S is the 19^th letter.
• H is the 8^th letter.

The code given for 'PUSH' is '1419176'. Let's see how this code might relate to the alphabetical positions:

• For P (position 16), the code part is 14. The difference is $16 - 14 = 2$.
• For U (position 21), the code part is 19. The difference is $21 - 19 = 2$.
• For S (position 19), the code part is 17. The difference is $19 - 17 = 2$.
• For H (position 8), the code part is 6. The difference is $8 - 6 = 2$.

We observe a consistent pattern: the code for each letter is obtained by subtracting 2 from its alphabetical position. The final code '1419176' is formed by concatenating these results.

Let's confirm:

• P: $16 - 2 = 14$
• U: $21 - 2 = 19$
• S: $19 - 2 = 17$
• H: $8 - 2 = 6$

Concatenating these gives 14, 19, 17, 6, resulting in '1419176'. The pattern is confirmed.

Applying the Pattern to 'HIKE'

Now, we need to apply the same pattern (alphabetical position minus 2) to the word HIKE.

First, let's find the alphabetical positions for the letters in 'HIKE':

• H is the 8^th letter.
• I is the 9^th letter.
• K is the 11^th letter.
• E is the 5^th letter.

Next, we apply the derived rule (subtract 2 from the position) to each letter:

• For H: Position is 8. Code value = $8 - 2 = 6$.
• For I: Position is 9. Code value = $9 - 2 = 7$.
• For K: Position is 11. Code value = $11 - 2 = 9$.
• For E: Position is 5. Code value = $5 - 2 = 3$.

Finally, we concatenate these resulting numbers (6, 7, 9, 3) to get the final code for 'HIKE'.

The code for 'HIKE' is '6793'.

Conclusion

Based on the identified pattern, the word 'HIKE' is written as '6793' in the given code language. This matches the second option.