The given expressions are
[tex]\begin{gathered} 24w^3u^7v^8 \\ 20w^6u \end{gathered}[/tex]The greatest common factor between the coefficients is 4 because that the greatest factor they have in common as you can observe below
[tex]\begin{gathered} 24=2\cdot2\cdot2\cdot3 \\ 20=2\cdot2\cdot5 \end{gathered}[/tex]The greatest common factor between variables is
[tex]w^3u[/tex]Hence, the greatest common factor of both expressions is
[tex]4w^3u[/tex]