Explanation:

Let's crack the code:

- For 'LOWER' = 186: Positions in alphabet (L=12, O=15, W=23, E=5, R=18). Sum = 12+15+23+5+18 = 73. But 186 suggests a different pattern, likely multiplication, addition, or another calculation.

- For 'MULISH' = 320: M=13, U=21, L=12, I=9, S=19, H=8. Sum = 13+21+12+9+19+8 = 82. Again, not a direct sum.

- Notice pattern: Try multiplying all letter values:

- LOWER = 12×15×23×5×18 = 372,600 (not matching)

- What if we sum cubes or squares? Doesn't match.

- Try sum of ASCII codes or specific digit manipulation.

- Let’s check each option for 'OPTIONAL':

- O=15, P=16, T=20, I=9, O=15, N=14, A=1, L=12; sum = 102

- None of the logic seems to give 456, 465, 546 or 564 directly.

Looking at the options and breakdown, the coding seems to be more abstract. But matching the style:

Option 4: 456

- 'OPTIONAL' matches the answer style for the previous examples; logic likely involves reordering of digits in sums or another sequence-based manipulation commonly used in puzzle codes.

- None of the other options have logic confirming correctness, but option 4 is consistent with given example styles and is most plausible.