Question

The managers discussed the plan that they would like to see____ next year

为什么不用to be carried out

Answer 1

would like to do本身就有将来的意思了，所以用carried out，不用加to be了。

Answer 2

感官性动词see/ hear/watch/listen to/observe+宾语+(to) do 表示听见看见全过程或者反复发生的事情
+doing 表示正在进行
+done 表示被动完成
例如
I often hear them quarrel
I hear them quarreling
I hear the song sung by him