three-way interaction plot for mixed effects regression model I am a relatively inexperienced R user and is a newbie here. I would like to ask for your advice regarding how to plot a three-way interaction graph in R.
My mixed effects regression model looks like this:
model1 <- lmer(score ~ TaskType * Language * Time + VocabSize + (1|ID), data= vocabtestscore)

TaskType is binary (1 and 2) and refers to the type of second language word learning task the participants completed. Language is also categorical (the students' first or second language) and refers to the language used in the glosses of the target words (words they didn't know) in the task. The study has a factorial design, so there are 2*2 = 4 word learning task conditions. Each participant is in only one of the four conditions. Finally, VocabSize refers to participants' previous vocabulary size, as measured by a test. This is the only continuous predictor.
After task completion, each student completed two post-tests of their knowledge of the target words: immediate and delayed post-tests.  Therefore, Time refers to the time of testing and is binary.
Based on the regression results, there is a significant three-way interaction between TaskType, Language, and Time. Therefore, I would like to plot a graph to illustrate the interaction.
I searched online and found that the code below might be the code I need:
emmip(model1 , Language ~ TaskType | Time, CIs=TRUE)   

And below is the graph I obtained:
https://imgur.com/a/flVNIfs
Did I plot the interaction correctly? What I am not sure is whether this interaction plot takes into account the fact that my model is a mixed effects model and the fact that VocabSize is present in the model.
I would appreciate any suggestions.

What you show seems fine. With a 2x2x2 interaction you have  8 estimates to display. You chose to show separate plots for immediate and delayed post-test times with four estimates in each, but in principle you could instead show separate plots for language or for task type. The choice depends on what you want to emphasize visually.
Don't forget that the display makes implicit assumptions about the value of VocabSize and the value of the random effect (ID). As neither of those is involved in an interaction (or random slope) involving your 3 interacting predictors, those assumptions just affect the specific values displayed on the y-axis. Check the emmeans help pages to make sure you know what those assumptions are; they should be reported in the legend of a figure like this.
