With a rank of 178 in the APPGECET 2024 for the ME (Mechanical Engineering) paper, you have a reasonable chance of securing a seat at JNTU Kakinada (JNTUK), but it depends on several factors:

1. **Previous Year Cutoffs**: Check the previous year’s cutoff ranks for Mechanical Engineering at JNTUK. If your rank is within or better than the previous year’s cutoffs, your chances are good. JNTUK generally has varying cutoffs based on the number of applicants and available seats.

2. **Counseling Process**: During the counseling process, seats are allocated based on rank, preference, and availability. Since you are ranked 178, you may be considered for one of the available seats, especially if you prioritize JNTUK in your choice list.

3. **Number of Seats**: Mechanical Engineering is a popular branch, and JNTUK offers several seats in this discipline. If there are many seats available and your rank is within the acceptable range, you are likely to get a seat.

4. **Special Categories**: If you belong to any reserved category or have specific preferences (like a particular specialization), it might also affect your chances.

Monitor the counseling schedule closely and stay in touch with the admission authorities to ensure you make the most of your rank.