When I try to install bioconductors using

if (!requireNamespace("BiocManager", quietly = TRUE))
    install.packages("BiocManager")
BiocManager::install(version = "3.10")

I am getting the following error:

The downloaded binary packages are in
    /var/folders/74/y92tqhzj0l98l6syjjl7vtcr0000gn/T//RtmpsTzyew/downloaded_packages
Old packages: 'nlme'
Update all/some/none? [a/s/n]: 
a
Warning: unable to access index for repository https://cran.rstudio.com/bin/macosx/el-capitan/contrib/3.6:
  cannot open URL 'https://cran.rstudio.com/bin/macosx/el-capitan/contrib/3.6/PACKAGES'
Package which is only available in source form, and may need
  compilation of C/C++/Fortran: ‘nlme’
Do you want to attempt to install these from sources? (Yes/no/cancel) Yes
installing the source package ‘nlme’

trying URL 'https://cran.rstudio.com/src/contrib/nlme_3.1-144.tar.gz'
Content type 'application/x-gzip' length 778660 bytes (760 KB)
==================================================
downloaded 760 KB

* installing *source* package ‘nlme’ ...
** package ‘nlme’ successfully unpacked and MD5 sums checked
** using staged installation
** libs
gfortran  -fPIC  -Wall -g -O2  -c chol.f -o chol.o
make: gfortran: No such file or directory
make: *** [chol.o] Error 1
ERROR: compilation failed for package ‘nlme’
* removing ‘/Library/Frameworks/R.framework/Versions/3.6/Resources/library/nlme’
* restoring previous ‘/Library/Frameworks/R.framework/Versions/3.6/Resources/library/nlme’

The downloaded source packages are in
    ‘/private/var/folders/74/y92tqhzj0l98l6syjjl7vtcr0000gn/T/RtmpsTzyew/downloaded_packages’
Warning message:
In install.packages(update[instlib == l, "Package"], l, repos = repos,  :
  installation of package ‘nlme’ had non-zero exit status

Any suggestions on how to resolve this issue?

You were asked if you want to try to install a source package that may contain C/C++ or Fortran code that will need to be compiled, to which you said 'Yes'. It then bombed out after trying to compile some Fortran code because you haven't set up your Mac to be able to do such things.

If you want to be able to compile on your Mac, you need to install XCode, which used to be sort of a pain, but maybe it's easier these days? I haven't used a Mac in years now, so I would just recommend doing a google search.