Explanation:

Let's break down the problem:

- The series is DY_ GMI__ YTG_ILDYT _MILD_ TGM_L.

- The answer choices are sequences of letters to fill the blanks.

- Let's check each blank:

- DY_

- GMI__

- YTG_

- ILDYT_

- MILD_

- TGM_L

Now, let's try option 1 (TLDGMIY) and fill sequentially:

1. DYT

2. GMIL

3. YTGD

4. ILDYTG

5. MILDM

6. TGMI

- If we observe, the pattern seems to be "TLDGMIY" and when used, the completed series becomes:

DYT GMIL YTGD ILDYTG MILDM TGMI

- This shows a repeated block in a cyclical manner. Option 1 fits.

- Now, let's try your answer, Option 3: TLDMGYI

1. DYT

2. GMIL

3. YTGD

4. ILDYTM

5. MILDG

6. TGMY

- Apparent from this, the block pattern breaks and doesn't fit smoothly in the pattern of the series.

So, the correct answer is:

- Option 1: TLDGMIY

This sequence fits the blank and sustains the cyclic pattern.

Option analysis:

- Option 1 (TLDGMIY): Maintains consistent letter pattern in the series.

- Option 2 (TDLGMYI): Letters disarranged, the sequence breaks.

- Option 3 (TLDMGYI): Your answer; order breaks the cyclic sequence.

- Option 4 (TLDYMIG): The sequence of letters does not fit pattern continuity.