Get the second value in the row if the dates match in R

Get the second value in the row if the dates match in R

I am in the trouble of getting the values which have the same dates from
two different data sources in R. The code is
#Monthly data
month_data <- c(580.11, 618.25, 641.24, 604.85, 580.86, 580.07, 632.97,
685.09, 754.50, 680.30, 698.37, 707.38, 480.11, 528.25,
541.24, 614.85, 680.86)
month_dates <- seq(as.Date("2001/06/01"), by = "1 months", length = 17)
month_data <- data.frame(month_dates, month_data)
#the dates_for_match is a data frame like the following
> dates_for_match
[[1]]
[1] "2001-08-01" "2001-09-01" "2001-10-01"
[[2]]
[1] "2001-11-01" "2001-12-01" "2002-01-01"
[[3]]
[1] "2002-02-01" "2002-03-01" "2002-04-01"
[[4]]
[1] "2002-05-01" "2002-06-01" "2002-07-01"
[[5]]
[1] "2002-08-01" "2002-09-01" "2002-10-01"
I want to use the dates_for_match list to get the values from month_data
that have the same dates.