My first attempt worked but part 2 took more than 100 seconds. 
So I got inspired by @Aetherus and @bjorng 's code and tips to rewrite it better. 
For instance:
putting obstacles only in the path actually walked by the guard.
And using MapSet but I reduced the streams. 
defmodule Aoc2024.Solutions.Y24.Day06 do
alias AoC.Input
def parse(input, _part) do
stream = Input.stream!(input, trim: true)
{start, obstacles} =
stream
|> Stream.with_index()
|> Enum.reduce({nil, MapSet.new()}, fn {line, x}, {start, obstacles} ->
line
|> String.to_charlist()
|> Stream.with_index()
|> Enum.reduce({start, obstacles}, fn
{?#, y}, {start, obstacles} -> {start, MapSet.put(obstacles, {x, y})}
{?^, y}, {_start, obstacles} -> {{x, y}, obstacles}
_, {start, obstacles} -> {start, obstacles}
end)
end)
row_end = Enum.count(stream) - 1
col_end = length(String.to_charlist(Enum.at(stream, 0))) - 1
{start, obstacles, row_end, col_end}
end
def part_one({{x, y}, obstacles, row_end, col_end}) do
path = build_path({?^, {x - 1, y}}, obstacles, MapSet.new([{x, y}]), row_end, col_end)
Enum.count(path)
end
def part_two({{x, y}, obstacles, row_end, col_end}) do
path = build_path({?^, {x - 1, y}}, obstacles, MapSet.new([{x, y}]), row_end, col_end)
Enum.reduce(path, 0, fn new_obstacle, counter ->
obstacles = MapSet.put(obstacles, new_obstacle)
limit = round(row_end * col_end / 2)
v = check_path({?^, {x - 1, y}}, obstacles, row_end, col_end, 0, limit)
v + counter
end)
end
defp build_path({direction, {x, y}}, obstacles, solution, row_end, col_end) do
cond do
x < 0 or x > row_end or y < 0 or y > col_end ->
solution
MapSet.member?(obstacles, {x, y}) ->
position = direct(direction, {x, y})
build_path(position, obstacles, solution, row_end, col_end)
true ->
position = continue(direction, {x, y})
build_path(position, obstacles, MapSet.put(solution, {x, y}), row_end, col_end)
end
end
defp check_path({direction, {x, y}}, obstacles, row_end, col_end, counter, limit) do
cond do
counter == limit ->
1
x < 0 or x > row_end or y < 0 or y > col_end ->
0
MapSet.member?(obstacles, {x, y}) ->
position = direct(direction, {x, y})
check_path(position, obstacles, row_end, col_end, counter, limit)
true ->
position = continue(direction, {x, y})
check_path(position, obstacles, row_end, col_end, counter + 1, limit)
end
end
defp direct(c, {x, y}) do
case c do
?^ -> {?>, {x + 1, y + 1}}
?> -> {?v, {x + 1, y - 1}}
?v -> {?<, {x - 1, y - 1}}
?< -> {?^, {x - 1, y + 1}}
end
end
defp continue(c, {x, y}) do
case c do
?^ -> {c, {x - 1, y}}
?> -> {c, {x, y + 1}}
?v -> {c, {x + 1, y}}
?< -> {c, {x, y - 1}}
end
end
end
I tried, but I couldn’t figure out when to stop in check_path therefor limit 
Solution for 2024 day 6
part_one: 4696 in 11.74ms
part_two: 1443 in 1.39s
thats so … fun … literally no improvements done on it whatsoever though 
… 
