$10$ am Tuesday to $10$ am Saturday $= 4$ days $= 96$ hours
$10$ am Saturday to $6$ pm Saturday $= 8$ hours
Time gained $= 15$ seconds $ \times (96 + 8) = 1560$ seconds
Converted into minutes $ = \dfrac{1560}{60}= 26$ minutes gain
Thus, time shown $= 6\;\text{pm} + 26\;\text{mins} = 6 : 26\;\text{pm}.$
So, the correct answer is $(C).$