The displacement of interest is the value of x at t=1 minus the value of x at t=0.
At t=1
... x = 4cos(π+π/4) = 4·(-√2)/2 = -2√2
At t=0
... x = 4cos(π/4) = 4·(√2)/2 = 2√2
Then the difference (displacement) is
... -2√2 -(2√2) = -4√2 ≈ -5.6569
