Use ratio or root test.
You see that the limit L of either ratio or root test is 0 and by that the series converges for all x.
in in case of ratio test you have
limit|(X-4)^(n+1)/n^(n+1). * n^(n)/(x-4)^(n)| = limit|(x-4)/n| = |x-4|*limit|1/n| = |x-4|*0 = 0 < 1 so absolutely convergent. Choice of X does not matter