Using ifelse a base-r solution
df$Category <- ifelse(df$Age<=3, "Infant", ifelse(df$Age<=6, "Toddler", ifelse(df$Age<=13, "Adolescence", ifelse(df$Age<=19, "Teenage", ifelse(df$Age<=59, "Adult", "Senior")))))
# -------------------------------------------------------------------------
# df
#     Id Age    Category
# 1   1   1      Infant
# 2   2   5     Toddler
# 3   3  10 Adolescence
# 4   4  12 Adolescence
# 5   5   3      Infant
# 6   6  23       Adult
# 7   7  55       Adult
# 8   8  42       Adult
# 9   9  92      Senior
# 10 10  78      Senior
# 11 11  33       Adult
# 12 12  44       Adult
# 13 13  25       Adult
# 14 14  13 Adolescence
# 15 15  10 Adolescence
# 16 16  19     Teenage
# 17 17  45       Adult
# 18 18  39       Adult
Using dplyr mutate and case_when
library(dplyr)
df <- df %>%
  mutate(Category =
  case_when(
    Age <=3 ~ "Infant", 
    Age <=6 ~ "Toddler",
    Age <=13 ~ "Adolesence",
    Age <=19 ~ "Teenage",
    Age <=59 ~ "Adult",
    TRUE ~ "Senior"
    
  )
)
# -------------------------------------------------------------------------
# df
#     Id Age   Category
# 1   1   1     Infant
# 2   2   5    Toddler
# 3   3  10 Adolesence
# 4   4  12 Adolesence
# 5   5   3     Infant
# 6   6  23      Adult
# 7   7  55      Adult
# 8   8  42      Adult
# 9   9  92     Senior
# 10 10  78     Senior
# 11 11  33      Adult
# 12 12  44      Adult
# 13 13  25      Adult
# 14 14  13 Adolesence
# 15 15  10 Adolesence
# 16 16  19    Teenage
# 17 17  45      Adult
# 18 18  39      Adult
# 
See the comments above as well as you need to provide a reproducible example to get a solution target towards your specific problem. Providing a reproducible example guarantees a quick response.
Sample Data
df <- data.frame(Id = seq(1,18,1), 
                 Age = c(1,5,10, 12, 3, 23, 55, 42, 92, 78, 33, 44, 25, 13, 10, 19, 45, 39))
Hope this helps.