Explanation:

To solve this letter analogy, we need to find the pattern of transformation from 'MGV' to 'HHA' and then apply the same pattern to 'LCT'. \nStep 1: Assign numerical positions to the letters of 'MGV' and 'HHA'.\nFor 'MGV': M is $13^{th}$, G is $7^{th}$, V is $22^{nd}$.\nFor 'HHA': H is $8^{th}$, H is $8^{th}$, A is $1^{st}$. \nStep 2: Determine the pattern for each letter position.\nFirst letter: M ($13$) to H ($8$). The difference is $8 - 13 = -5$.\nSecond letter: G ($7$) to H ($8$). The difference is $8 - 7 = +1$.\nThird letter: V ($22$) to A ($1$). Considering the alphabet wraps around, A can also be $27^{th}$. So, $27 - 22 = +5$. Alternatively, $1 - 22 = -21$. The $+5$ pattern is more common in such series.\nThus, the pattern is $(-5, +1, +5)$. \nStep 3: Apply the pattern to 'LCT'.\nFor 'LCT': L is $12^{th}$, C is $3^{rd}$, T is $20^{th}$. \nFirst letter: L ($12$) $- 5 = 7^{th}$ letter, which is G.\nSecond letter: C ($3$) $+ 1 = 4^{th}$ letter, which is D.\nThird letter: T ($20$) $+ 5 = 25^{th}$ letter, which is Y. \nSo, 'LCT' transforms to 'GDY'. \nStep 4: Evaluate the options.\nOption A: HDZ. This is incorrect as it does not follow the established pattern.\nOption B: GDY. This matches our calculated result.\nOption C: IDY. This is incorrect.\nOption D: IDZ. This is incorrect. \nTherefore, the correct option is 'GDY'.