To calculate the forecast for Year $2$ using a smoothing constant of $0\mathrm{.}6,$ we use the formula

Forecast for Year $2=(1-$ Smoothing Constant$)$ Actual Demand in Year $1+$ Smoothing Constant Forecast for Year $1$

Forecast for Year $2=(1-0\mathrm{.}6)45+0\mathrm{.}641=0\mathrm{.}445+0\mathrm{.}641=18+24\mathrm{.}6=42\mathrm{.}6$

Step $2$: Repeat the process for the following years, using the previous year's forecast as the starting point.

For Year $3$:

Forecast for Year $3=(1-0\mathrm{.}6)50+0\mathrm{.}642\mathrm{.}6=0\mathrm{.}450+0\mathrm{.}642\mathrm{.}6=20+25\mathrm{.}56=45\mathrm{.}56$

For Year $4$:

Forecast for Year $4=(1-0\mathrm{.}6)52+0\mathrm{.}645\mathrm{.}56=0\mathrm{.}452+0\mathrm{.}645\mathrm{.}56=20\mathrm{.}8+27\mathrm{.}336=48\mathrm{.}136$

For Year $5$:

Forecast for Year $5=(1-0\mathrm{.}6)56+0\mathrm{.}648\mathrm{.}136=0\mathrm{.}456+0\mathrm{.}648\mathrm{.}136=22\mathrm{.}4+28\mathrm{.}8816=51\mathrm{.}2816$

For Year $6$:

Forecast for Year $6=(1-0\mathrm{.}6)58+0\mathrm{.}651\mathrm{.}2816=0\mathrm{.}458+0\mathrm{.}651\mathrm{.}2816=23\mathrm{.}2+30\mathrm{.}76896=53\mathrm{.}96896$