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width   =   4  yards

length   =   5$\frac23$  yards

area   =   width  *  length

                                                      Plug in the given values for width and length.

area   =   4 yards  *  5$\frac23$  yards

area  =   (4 * 5$\frac23$)  square yards

                                                      Convert  5$\frac23$  to  $\frac{17}{3}$

area  =   (4 * $\frac{17}3$)  square yards

                                                      Multiply.

area   =   $\frac{68}{3}$   square yards

                                                      Convert  $\frac{68}3$  to  22$\frac{2}{3}$

area   =   22$\frac23$  square yards