To simplify the given Boolean expression, let's break it down step by step:

Step 1: Simplify the expression E(E F)
- In this expression, E is being multiplied by (E F).
- According to the distributive property of Boolean algebra, E(E F) is equivalent to EE EF.
- Since E is being multiplied by itself (EE), it simplifies to just E.
- Thus, the expression E(E F) simplifies to E EF.

Step 2: Simplify the expression DE
- In this expression, D is being multiplied by E.
- Since there are no common variables in this expression, it cannot be simplified further.

Step 3: Simplify the expression D(E F)
- In this expression, D is being multiplied by (E F).
- According to the distributive property of Boolean algebra, D(E F) is equivalent to DE DF.
- Since we have already simplified DE in Step 2, the expression D(E F) simplifies to E DF.

Step 4: Simplify the expression E DF
- In this expression, E is being multiplied by DF.
- Since there are no common variables in this expression, it cannot be simplified further.

Step 5: Combine the simplified expressions from Steps 1, 2, and 4
- The simplified expressions from Steps 1, 2, and 4 are: E EF, DE, and E DF, respectively.
- Combining these expressions, we get: (E EF) DE (E DF).

Step 6: Further simplify the expression (E EF) DE (E DF)
- In this expression, we have three terms: (E EF), DE, and (E DF).
- Since there are no common variables among these terms, we cannot simplify the expression any further.

Therefore, the simplified Boolean expression is E DF, which corresponds to option 'C'.