Explanation:

To find the value of 'MASTER', we need to determine the coding rule from the given examples: V=44 and FAT=54. \nStep 1: Analyze the coding for 'V'.\nThe letter V is the $22^{nd}$ letter in the alphabet.\nGiven V = $44$. We can see that $22 \times 2 = 44$.\nThis suggests the rule might be (positional value of letter) $\times 2$. \nStep 2: Analyze the coding for 'FAT'.\nF is the $6^{th}$ letter.\nA is the $1^{st}$ letter.\nT is the $20^{th}$ letter.\nSum of positional values: $6 + 1 + 20 = 27$.\nGiven FAT = $54$. We can see that $27 \times 2 = 54$.\nThis confirms the rule: (Sum of positional values of all letters) $\times 2$. \nStep 3: Apply the rule to 'MASTER'.\nAssign positional values to each letter in 'MASTER':\nM = $13^{th}$\nA = $1^{st}$\nS = $19^{th}$\nT = $20^{th}$\nE = $5^{th}$\nR = $18^{th}$ \nSum of positional values: $13 + 1 + 19 + 20 + 5 + 18 = 76$. \nStep 4: Multiply the sum by 2. $76 \times 2 = 152$. \nStep 5: Evaluate the options.\nOption A: $146$. This is incorrect.\nOption B: $152$. This matches our calculated result.\nOption C: $158$. This is incorrect.\nOption D: $162$. This is incorrect. \nTherefore, 'MASTER' = $152$.