Correcting error messages emitted by ListPlot

Problem 1: The source of the error is the second ListLinePlot. You can see this because if you click on the orange bubble {...} on the error and select Show Stack Trace you get this:

> Message[ListLinePlot::lpn, 3.6]

> ListLinePlot[18/5, PlotStyle -> RGBColor[0, 1, 0]]

You are trying to plot a single number 18/5, the mean. You need to provide at least two points to get a line in ListLinePlot. To fix this use ListLinePlot[{{0,mean},{Length[ang],mean}}].

Problem 2: You need to use AllTrue instead of All when checking the list of strings.

Also you can shorten your If statements. If they fail and the Print's are triggered, then integer and string get assigned the return value of Print which is Null. I assume you really want False.

Problem 3: You want to pass in strings into your function {"i", "am", "so", "confused"}, not the list of symbols {i,am,so,confused}

Putting it all together:

fungsi[ang_, str_] := Module[{integer, string, max, mean, gambar},
  integer = AllTrue[ang, IntegerQ];
  string = AllTrue[str, StringQ];
  If[Not[integer], Print["not integers"]];
  If[Not[string], Print["not strings"]];
  max = Max[ang];
  mean = Mean[ang];
  gambar = 
   Show[
    ListLinePlot[ang, PlotStyle -> Blue], 
    ListLinePlot[{{0,mean},{Length[ang],mean}}, PlotStyle -> {Green,Dashed}],
    ListLinePlot[{{0,max}, {Length[ang],max}}, PlotStyle -> Red]
   ]
 ]
fungsi[{1, 2, 3, 4, 8}, {"i", "am", "so", "confused"}]

You can also add lines and other graphics to plots using Epilog like this:

ListLinePlot[{1, 2, 3, 4}, 
 Epilog -> {Purple, Dashed, Line[{{0, 2}, {4, 2}}]}]