You could've moved the 2 in the c(2a+c) to outside of the parenthesis, because then you can cancel out the 2a on the top and bottom (which you see on the next step). This leaves you with just a+6 / a+3.

c*(2a+6) gives you 2ca+6c (using distributive method). Both of these terms have a common factor of 2c, which means that we can factor out 2c. (2ca)/(2c)=a, and (6c)/(2c)=3. We then put this all together, leaving the common factor outside of the parentheses to get 2c(a+3) as the bottom number in the fraction. Hope this helps!