Here is one method using the dplyr library.
Df <- data.frame(A=c(2,3,9),B=c(5,4,8),C=c(4,5,7),D=c(4,6,6),E=c(5,7,7),Mean=c(4,5,7))
Df
#> A B C D E Mean
#> 1 2 5 4 4 5 4
#> 2 3 4 5 6 7 5
#> 3 9 8 7 6 7 7
library(dplyr,warn.conflicts = FALSE)
Df %>% rowwise() %>% mutate(Pos = which(c_across(A:E) > Mean)[1])
#> # A tibble: 3 x 7
#> # Rowwise:
#> A B C D E Mean Pos
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <int>
#> 1 2 5 4 4 5 4 2
#> 2 3 4 5 6 7 5 4
#> 3 9 8 7 6 7 7 1
Created on 2020-12-09 by the reprex package (v0.3.0)