Answer
The point of intersection is (0,2)
Work Step by Step
When plotting the two equations 2^(x+1) and 2^(1-x) they both line up perfectly crossing at (0,2)
When doing an xy chart for 2^(x+1) plugging in 0 for x makes the graph cross at (0,2)
x y
0 2
1 4
2 8
Now an xy chart for 2^(1-x)
x y
0 2
1 1
2 1/2
This proves that the lines cross at (0,2)