The simplest way to launch a playlist--if your media player supports it--is to use the Shortcut action. When configuring the command, tap the magnifying glass and select the playlist shortcut for your media app. Some media players don't have shortcuts and some have shortcuts that are incompatible with the Tasker action. Unfortunately for you, Media Monkey has incompatible shortcuts, so you have to do it the hard way.
The more complex way requires AutoInput. You can use Tasker to launch Media Monkey, then use AutoInput to navigate to and launch the playlist. Below is an example of how I did this with Samsung Music Player, which doesn't have shortcuts.
Task: Samsung Vocal
<Force screen to portrait orientation>
A1: Force Rotation [
Mode: Portrait ]
<Open the music player>
A2: Launch App [
Package/App Name: Samsung Music
Always Start New Copy: On ] <<<<<<<<<<<<<<< Critical: This must be ON so AutoInput will be starting in the same place each time
<Give it time to open>
A3: Wait [
MS: 0
Seconds: 1
Minutes: 0
Hours: 0
Days: 0 ]
<Select the playlist>
A4: AutoInput Action [
Configuration: Type: Text
Value: Boson <<<<<<<<<<<<<<<<<< This is the name of the playlist
Action : Click
Timeout (Seconds): 23
Structure Output (JSON, etc): On ]
<Tap the shuffle button>
A5: AutoInput Action [
Configuration: Type: Id
Value: com.sec.android.app.music:id/icon_shuffle
Action : Click
Timeout (Seconds): 23
Structure Output (JSON, etc): On ]
<Return to the icon screen> <<<<<<<<<<<<<<<<<<<< Omit this step if you want to stay in the player; I want to go back to the launcher
A6: Go Home [
Page: 0 ]
<Allow screen to rotate normally>
A7: Force Rotation [
Mode: Off ]