In a probability experiment that records the sum of the numbers on the upper faces of the dice after they become stationary, the outcome with the greatest probability is...
That makes it a poor problem.
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The coefficients tell us the number of way we can get the various sums when four dice are used. For example the term $\displaystyle 146x^{14}$ tells us there are 146 ways to throw a fourteen.
You can change the power 4 in $\displaystyle \left( {\sum\limits_{k = }^6 {x^k } } \right)^4 $ to find out the numbers for any number of dice.