Ooff! This one's tricky because you've basically got a variable value encoded in the column names, and I haven't come up with a better solution… Thought having a reprex showing the output might help, though 
library(tidyverse)
df <- tibble(
key = 1:2, x_1 = paste("x", 1:2, sep = ""), x_2 = paste("x", 3:4, sep = ""),
y_1 = paste("y", 1:2, sep = ""), y_2 = paste("y", 3:4, sep = ""),
z_1 = paste("z", 1:2, sep = ""), z_2 = paste("z", 3:4, sep = "")
)
df
#> # A tibble: 2 x 7
#> key x_1 x_2 y_1 y_2 z_1 z_2
#> <int> <chr> <chr> <chr> <chr> <chr> <chr>
#> 1 1 x1 x3 y1 y3 z1 z3
#> 2 2 x2 x4 y2 y4 z2 z4
# Desired output
df_long <- tibble(key = rep(1:2, 2), x = paste("x", 1:4, sep = ""), y = paste("y", 1:4, sep = ""), z = paste("z", 1:4, sep = ""))
df_long
#> # A tibble: 4 x 4
#> key x y z
#> <int> <chr> <chr> <chr>
#> 1 1 x1 y1 z1
#> 2 2 x2 y2 z2
#> 3 1 x3 y3 z3
#> 4 2 x4 y4 z4
# Long solution
pivot_longer(df, cols = -key, names_to = c("var", "rep"), names_pattern = ("(.)_(.)"), values_to = "val") %>%
pivot_wider(names_from = "var", values_from = "val")
#> # A tibble: 4 x 5
#> key rep x y z
#> <int> <chr> <chr> <chr> <chr>
#> 1 1 1 x1 y1 z1
#> 2 1 2 x3 y3 z3
#> 3 2 1 x2 y2 z2
#> 4 2 2 x4 y4 z4
Created on 2020-06-03 by the reprex package (v0.3.0.9001)