Regarding both pairwise comparisons and adjustment for multiple comparisons, doesn't ````emmeans```` solution work?

````
library(emmeans)
em1<-emmeans(m2, ~cyl) #this gives you estimated marginal means of disp at different levels of cyl from the model m2
em1
contrast(em1, "pairwise", simple="each", combine=T, adjust="sidak") 

#this gives you all pairwise comparisons with Sidak's multiple comparison adjustment.
#you can also choose other adjustments such as bonferroni but sidak is probably most commonly used
#You can also choose adjust="none" in which case p-values are not adjusted (and you see that the comparison values in the emmeans contrasts between cyl=4 and other groups are identical to the regression summary table).
````
Re: 
>From the table above, the p-value of $βcyl=6$ is 0.036<0.05
Could I interpret this value directly and conclude: "The mean disp with cyl=6 is different from that with cyl=4 (baseline) after controlling drat"

Yes, but for those values, no p-value adjustment for multiple comparisons has been applied. This comparison is actually no longer significant after applying sidak correction.