Number of ways of selecting 6 shoes, out of 8 pairs of shoes, having exactly two pairs is

From 8 pairs of shoes 2 pairs can be selected in ${ }^8{C}_2$ ways

From the  remaining 6 pairs 2 pairs can be selected in${ }^6{C}_2$ ways  and from each select one from each pair in 2² ways

Required number of ways ${=}^8{C}_2{\times }^6{C}_2\times 2^2=1680$