You can do it with ggplot_build():
library(ggplot2)
dat = data.frame(a = c(5.5,7,4,20,4.75,6,5,8.5,10,10.5,13.5,14,11))
p=ggplot(dat, aes(x=a)) +
geom_histogram(aes(y=..density..),breaks = seq(4,20,by=2))+xlab("Required Solving Time")
ggplot_build(p)$data
#[[1]]
# y count x xmin xmax density ncount ndensity PANEL group ymin ymax colour fill size linetype alpha
#1 0.19230769 5 5 4 6 0.19230769 1.0 26.0 1 -1 0 0.19230769 NA grey35 0.5 1 NA
#2 0.03846154 1 7 6 8 0.03846154 0.2 5.2 1 -1 0 0.03846154 NA grey35 0.5 1 NA
#3 0.07692308 2 9 8 10 0.07692308 0.4 10.4 1 -1 0 0.07692308 NA grey35 0.5 1 NA
#4 0.07692308 2 11 10 12 0.07692308 0.4 10.4 1 -1 0 0.07692308 NA grey35 0.5 1 NA
#5 0.07692308 2 13 12 14 0.07692308 0.4 10.4 1 -1 0 0.07692308 NA grey35 0.5 1 NA
#6 0.00000000 0 15 14 16 0.00000000 0.0 0.0 1 -1 0 0.00000000 NA grey35 0.5 1 NA
#7 0.00000000 0 17 16 18 0.00000000 0.0 0.0 1 -1 0 0.00000000 NA grey35 0.5 1 NA
#8 0.03846154 1 19 18 20 0.03846154 0.2 5.2 1 -1 0 0.03846154 NA grey35 0.5 1 NA
p + geom_text(data = as.data.frame(ggplot_build(p)$data),
aes(x=x, y= density , label = round(density,2)),
nudge_y = 0.005)
