Explanation:

- The letter series given is: D E _ W G _ E F _ G D E F U _ D _ F T G.

- Our task is to fill in the blanks with the correct sequence of letters from the options provided.

- Look for repeating sequences or patterns in the given series.

- The visible pattern is:

- D E, followed by W G

- E F, followed by G

- D E F, followed by U

- D, followed by F

- Align each option with these patterns to find the best fit.

Evaluating Option 1: F D G V E

- This doesn't match the repeating pattern determined.

Evaluating Option 2: F D V G E

- This aligns well when placed into blanks and complements each repeating sequence.

Evaluating Option 3: D F F E V

- This doesn't align properly with the established patterns.

Evaluating Option 4: D F V G F

- This doesn't match the entire repeating sequence correctly.

Correct Answer: Option 2: F D V G E