derive multiple columns from multiple columns in r

Assuming the integrity of your structure and naming conventions, you can select the x and y variables, multiple them together as a group, and then assign back to z.

var_i <- 1:3

testa[paste0("z", var_i)] <- testa[paste0("x", var_i)] * testa[paste0("y", var_i)]

  x1 x2 x3 x4 y1 y2 y3 z1 z2 z3
1  1  2  3  A  1  2  3  1  4  9
2  2  3  4  B  2  3  4  4  9 16
3  3  4  5  C  3  4  5  9 16 25
4  4  5  6  D  4  5  6 16 25 36
5  5  6  7  E  5  6  7 25 36 49
6  6  7  8  F  6  7  8 36 49 64

If we want to do this automatically, a tidyverse option is

library(dplyr)
library(stringr)
testa <- testa %>% 
   mutate(across(x1:x3,  ~ .x * get(str_replace(cur_column(), "x",
        "y")), .names = "{str_replace(.col, 'x', 'z')}"))

-output

testa
  x1 x2 x3 x4 y1 y2 y3 z1 z2 z3
1  1  2  3  A  1  2  3  1  4  9
2  2  3  4  B  2  3  4  4  9 16
3  3  4  5  C  3  4  5  9 16 25
4  4  5  6  D  4  5  6 16 25 36
5  5  6  7  E  5  6  7 25 36 49
6  6  7  8  F  6  7  8 36 49 64