Explanation:

Let’s break down the pattern:

- LIBERTY = 4221824364050

- Assign numbers to each letter: L, I, B, E, R, T, Y

- It seems each letter is replaced with a pair of digits.

Let’s try mapping:

- L = 42

- I = 21

- B = 82

- E = 43

- R = 64

- T = 05

- Y = 0

Applying the same pairs to SLAVERY:

- S = ?

- L = 42

- A = ?

- V = ?

- E = 43

- R = 64

- Y = 50

Let’s check options:

1. 26222436384450

2. 22262438365040

3. 26224233684540

4. 22242636384050

Now, let's see if any option uses same coding for L,E,R,Y as per LIBERTY:

- In 'LIBERTY', L-E-R-Y is 42-43-64-50

- Option 1: 26 22 24 36 38 44 50

- Here, 44-50 at end, but does not align with 'LIBERTY' code for E-R-Y.

- Option 2: 22 26 24 38 36 50 40

- Option 3: 26 22 42 33 68 45 40

- Option 4: 22 24 26 36 38 40 50

Let’s match positions:

- Positions for 'SLAVERY': S-L-A-V-E-R-Y

Comparing 'LIBERTY' pattern L, E, R, Y:

- 'L' always coded as 42

- 'E' as 43

- 'R' as 64

- 'Y' as 50

Find the code that matches those for L, E, R, Y:

- Looking at the options, none match the exact sequence for E, R, Y from LIBERTY.

- But Option 1 and Option 3 have '50' at the end for Y.

If we look only at the mapping, Option 4 ends with 40 50, but 'Y' is coded as '50' in 'LIBERTY' so 50 should be last. 'E' in 'LIBERTY' is 43, and in all options above, only option 3 (at 5th position) has 33 or 38, not 43.

By rechecking, it looks as though the code mapping isn't clear from the given data.

But, based on direct matching with 'LIBERTY', none match perfectly.

- Option 4: 22242636384050 ends with 50, which matches 'Y' in 'LIBERTY' and uses 36 and 38, which could fit for 'R' and 'E' (if pattern adjusted).

- So, Option 4 is the closest match and most logical fit given ending in 50.

Correct answer:

- Option 4: 22242636384050

Summary:

- Each letter seems matched to a unique two-digit code.

- The code for 'LIBERTY' can be used to match positions for 'SLAVERY'.

- 'Y' always coded as '50'.

- Option 4 best fits the positional and numeric clues from 'LIBERTY'.