(-1/3)√18c^5 * (-6√8c^9)

2√144c^14 ---> I came until here but then didn't know how to proceed.

After that, you should get:

2 * 12c^8(I think it's eight)

and then

24c^8

Sorry, you should look up how to downsize the exponent. My textbook does not explain that part at all.