It is better to reshape your data into long format. You can do that with for example the melt function of the reshape2 package (alternatives are reshape from base R, melt from data.table (which is an extended implementation of the melt function of reshape2) and gather from tidyr).
Using your dataset:
# load needed libraries
library(reshape2)
library(ggplot2)
# reshape your data into long format
nyxlong <- melt(nyx, id=c("Number"))
# make the plot
ggplot(nyxlong) +
  geom_bar(aes(x = Number, y = value, fill = variable), 
           stat="identity", position = "dodge", width = 0.7) +
  scale_fill_manual("Result\n", values = c("red","blue"), 
                    labels = c(" Yresult", " Xresult")) +
  labs(x="\nNumber",y="Result\n") +
  theme_bw(base_size = 14)
which gives the following barchart:
