i) compute the Taylor series for $\ln(1-x)$ and then make the substitution $x\rightarrow \dfrac x 2$ and then add $\ln(2)$ as the "0th" term.
This is a very simple Taylor series you should have no trouble computing.
Once you find the terms of the series apply the ratio test to determine the radius of convergence as usual.
ii) as $\ln(6-x)=\ln(2 - (x-4))$ you can use the series you found in (i) for $\ln(2-x)$ but now make the substitution
$x \rightarrow (x-4)$
iii) should be straightforward.