In a double-slit experiment the light has a wavelength of 550 nm…

Step 1. The extra path. $(\mu - 1)t = (1.58 - 1) \times 4.2\ \mu\text{m} = 2.44\ \mu\text{m}$.

Step 2. The fringes. $\dfrac{2.44\ \mu\text{m}}{550\ \text{nm}} = 4.43$ fringes.

Step 3. The fringe width. $\beta = \dfrac{\lambda D}{d} = \dfrac{550 \times 10^{-9}\ \text{m} \times 1.60\ \text{m}}{0.40 \times 10^{-3}\ \text{m}} = 2.20\ \text{mm}$. The sheet does not change it.

Step 4. The shift. $\Delta y = 4.43 \times 2.20\ \text{mm} = 9.74\ \text{mm}$, towards the covered slit.