You need to convert date from character to appropriate date format. Then you can group data by month & year.
df <- data.frame(date=c('02/01/2021', '18/01/2021', '26/02/2021', '16/02/2021'),
b=c(1, 2, 3, 5))
df1 <- data.frame(date=c('14/02/2021', '27/04/2021', '06/06/2021', '15/01/2021'),
b=c(3, 4, 1, 1))
df3 <- rbind(df, df1)
library(dplyr)
library(lubridate)
df3 %>%
mutate(date = as_date(date, format="%d/%m/%Y")) %>%
group_by(month_year = floor_date(date, "month")) %>%
summarize(sum=sum(b))
# if you really want to present date as Month & Year
df3 %>%
mutate(date = as_date(date, format="%d/%m/%Y")) %>%
group_by(month_year = floor_date(date, "month")) %>%
summarize(sum=sum(b)) %>%
mutate(month_year = zoo::as.yearmon(month_year))