解：?$\begin {cases}x + 2y = 6&①\\2x - 2y+mx = 8&②\end {cases}$?
① + ②得：?$x + 2y+2x - 2y+mx = 6 + 8，$?
即?$(3 + m)x = 14，$?所以?$x=\frac {14}{3 + m}。$?
?$ $?由?$①$?得?$y = 3-\frac {x}{2}。$?
因?yàn)榉匠探M有整數(shù)解，且?$m $?是整數(shù)，?$x$?是偶數(shù)，
所以?$3 + m=\pm 1$?或?$3 + m=\pm 7$?
?$ $?當(dāng)?$3 + m = 1$?時(shí)，?$m=-2，$?此時(shí)
?$x = 14，$??$y = 3 - 7=-4；$?
?$ $?當(dāng)?$3 + m=-1$?時(shí)，?$m=-4，$?此時(shí)
?$x=-14，$??$y = 3 + 7 = 10；$?
?$ $?當(dāng)?$3 + m = 7$?時(shí)，?$m = 4，$?此時(shí)
?$x = 2，$??$y = 3 - 1 = 2；$?
?$ $?當(dāng)?$3 + m=-7$?時(shí)，?$m=-10，$?此時(shí)
?$x=-2，$??$y = 3 + 1 = 4；$?
綜上，整數(shù)?$m $?的值為?$-2$?或?$-4$?或?$-10$?或?$4。$?
