Is this what you want?
library(tidyverse)
dataset <- data.frame(
lotacc = c(1, 1, 1, 1, 1, 0.84, 0.938),
Started = c(14.28,20.16,37.39,83.66,95.4,104.8,104.8),
Finished = c(14.28,20.16,37.39,83.66,95.4,88,98.3),
Scrap = c(0,0, 0, 0, 0,16.8,6.5),
name = as.factor(c("KBP82", "KBP82", "KBP82", "KBP82","KBP82","KBP82","KBP82")),
subname = as.factor(c("BL17299425","BL18023812","BL18353300","BL19197009","EMBL19023001","EMBL19351646","EMBL19333591"))
)
dataset %>%
mutate(Scrap = Scrap * 8) %>%
gather(group, value, c(Scrap, Started, Finished)) %>%
mutate(name = paste(name, group)) %>%
ggplot(aes(x = as.numeric(subname), y = value, color = name, linetype = name)) +
geom_line() +
geom_point() +
scale_x_continuous(breaks = as.numeric(dataset$subname),
labels = as.character(dataset$subname)) +
scale_y_continuous("Started & Finished",sec.axis = sec_axis(~ ./8, name = "BLScrap")) +
theme_classic() +
theme(axis.text.x = element_text(angle=-90, vjust=0.5, hjust=0)) +
labs(title = "ART Results",
x = "Subname")

Created on 2020-01-24 by the reprex package (v0.3.0.9000)
If it isn't, maybe you could try to DM me an explain your issue in Spanish because honestly, I'm having problems understanding what you are writing.