division of a fraction is the equivalent of multiplying by its reciprocal
ex.
[tex]\frac{\frac{A}{B} }{\frac{C}{D}}=\frac{A}{B} *\frac{D}{C}[/tex]
i suggest you try to remember this concept
in terms of your question
[tex]\frac{\frac{4c-12}{4c+8}}{\frac{c-3}{c^2-4}}= \frac{4c-12}{4c+8} *\frac{c^2 -4}{c-3}[/tex]
from this point, just multiple the numerators together and denominators together, then simplify if necessary
fyi- difference of squares
[tex]x^2-b^2 = (x-b)(x+b)[/tex]
relating that to
[tex]c^2-4 = c^2 -2^2 = (c-2)(c+2)[/tex]
also a side note, you might want to factor out the 4 first in the top fraction
