Hey there!
I also think you have the correct answer. All you need to do to distribute these two terms is multiply them directly, since there are only two. If you multiply each like term together then combine them, you'll get [tex]24b^5c^7[/tex].
[tex]3 * 8 = 24[/tex]
[tex]b^2 * b^3 = b^5[/tex]
[tex]c*c^6 = c^7[/tex]
Hope this helped you out! :-)