quest_number is a numeric variable, so you can't compare it to characters (i.e. 7 != "7"), also, I suspect you want to treat that variable as a factor so you would have to convert it, see this example (BTW this would be a proper reprex for your issue).
library(tidyverse)
survey_data <- tibble::tribble(
~quest_number, ~numbered_level, ~response_level, ~demo_breakdown, ~est_percentage,
7L, 6, "Often", "age_18_34", 21,
7L, 5, "Sometimes", "age_18_34", 25,
7L, 4, "Rarely", "age_18_34", 19,
7L, 3, "Never, but open to it", "age_18_34", 14,
7L, 2, "Never, and not open to it", "age_18_34", 21,
7L, 1, "No answer", "age_18_34", 0,
8L, 6, "Often", "age_18_34", 13,
8L, 5, "Sometimes", "age_18_34", 35,
8L, 4, "Rarely", "age_18_34", 30,
8L, 3, "Never, but open to it", "age_18_34", 8,
8L, 2, "Never, and not open to it", "age_18_34", 14,
8L, 1, "No answer", "age_18_34", 0
)
survey_data %>%
filter(quest_number %in% c(7, 8), demo_breakdown == "age_18_34") %>%
ggplot() +
geom_line(mapping = aes(x = numbered_level, y = est_percentage, color = as.factor(quest_number)))

Created on 2019-12-08 by the reprex package (v0.3.0.9000)
It seems like you need to work a little bit on your basic R skills, I would recommend this free on-line book for covering the basics