解：?$(1)$?當(dāng)?$m=4$?時(shí)，?$BC=4$?
又∵?$AB=6$?，∴?$AC=4+6=10$?
又?$M$?為線段?$AC$?的中點(diǎn)，∴?$AM=MC=5$?
∴?$BM=AB-AM=6-5=1$?
?$(2)$?∵?$AB=6$?，?$BC=m$?，∴?$AC=6+m$?
∵?$M$?為線段?$AC$?的中點(diǎn)，∴?$AM=MC=\frac {6+m}{2}$?
①如圖，當(dāng)點(diǎn)?$D$?在線段?$BC$?上，點(diǎn)?$M$?在點(diǎn)?$D$?的左邊時(shí)
?$CD=n$?，?$DM=MC-CD=\frac {6+m}2-n=\frac {6+m-2n}{2}$?
②如圖，當(dāng)點(diǎn)?$D$?在線段?$BC$?上，點(diǎn)?$M$?在點(diǎn)?$D$?的右邊時(shí)
?$CD=n$?，?$DM=CD-MC=n-\frac {6+m}2=\frac {2n-6-m}{2}$?
③如圖，當(dāng)點(diǎn)?$D$?在?$l$?上且在點(diǎn)?$C$?的右側(cè)時(shí)
?$CD=n$?，?$DM=MC+CD=\frac {6+m}2 +n=\frac {6+m+2n}{2}$?
