Open conda shell prompt. (On Windows Anaconda Powershell Prompt)

You first check

conda search python

You will get all the supported versions. It may look like:

Loading channels: done
# Name                       Version           Build  Channel
python                        2.7.13     h1b6d89f_16  pkgs/main
python                        2.7.13     h9912b81_15  pkgs/main
python                        2.7.13     hb034564_12  pkgs/main
python                        2.7.14     h2765ee6_18  pkgs/main
python                        2.7.14     h3e68818_15  pkgs/main
python                        2.7.14     h4084c39_22  pkgs/main
python                        2.7.14     h4a10d90_30  pkgs/main
python                        2.7.14     h4a10d90_31  pkgs/main
python                        2.7.14     h59f5a59_20  pkgs/main
python                        2.7.14     h819644d_16  pkgs/main
python                        2.7.14     h8c3f1cb_23  pkgs/main
python                        2.7.15      h2880e7c_2  pkgs/main
python                        2.7.15      h2880e7c_3  pkgs/main
python                        2.7.15      h2880e7c_4  pkgs/main
python                        2.7.15     hcb6e200_15  pkgs/main
python                        2.7.15      hcb6e200_5  pkgs/main
python                        2.7.15      hcb6e200_7  pkgs/main
python                        2.7.15      he216670_0  pkgs/main
python                        2.7.16      hcb6e200_0  pkgs/main
python                        2.7.17      h930f6bb_0  pkgs/main
python                         3.5.4     h1357f44_23  pkgs/main
python                         3.5.4     hc495aa9_21  pkgs/main
python                         3.5.4     hd3c4935_11  pkgs/main
python                         3.5.4     hdec4e59_20  pkgs/main
python                         3.5.4     hedc2606_15  pkgs/main
python                         3.5.5      h0c2934d_0  pkgs/main
python                         3.5.5      h0c2934d_1  pkgs/main
python                         3.5.5      h0c2934d_2  pkgs/main
python                         3.5.6      he025d50_0  pkgs/main
python                         3.6.2     h09676a0_15  pkgs/main
python                         3.6.2     h6679aeb_11  pkgs/main
python                         3.6.3      h210ce5f_2  pkgs/main
python                         3.6.3      h3389d20_0  pkgs/main
python                         3.6.3      h3b118a2_4  pkgs/main
python                         3.6.3      h9e2ca53_1  pkgs/main
python                         3.6.4      h0c2934d_2  pkgs/main
python                         3.6.4      h0c2934d_3  pkgs/main
python                         3.6.4      h6538335_0  pkgs/main
python                         3.6.4      h6538335_1  pkgs/main
python                         3.6.5      h0c2934d_0  pkgs/main
python                         3.6.6      hea74fb7_0  pkgs/main
python                         3.6.7      h33f27b4_0  pkgs/main
python                         3.6.7      h33f27b4_1  pkgs/main
python                         3.6.7      h9f7ef89_2  pkgs/main
python                         3.6.8      h9f7ef89_0  pkgs/main
python                         3.6.8      h9f7ef89_1  pkgs/main
python                         3.6.8      h9f7ef89_7  pkgs/main
python                         3.6.9      h5500b2f_0  pkgs/main
python                         3.7.0      hea74fb7_0  pkgs/main
python                         3.7.1      h33f27b4_3  pkgs/main
python                         3.7.1      h33f27b4_4  pkgs/main
python                         3.7.1      h8c8aaf0_6  pkgs/main
python                         3.7.1      he44a216_5  pkgs/main
python                         3.7.2      h8c8aaf0_0  pkgs/main
python                         3.7.2     h8c8aaf0_10  pkgs/main
python                         3.7.2      h8c8aaf0_2  pkgs/main
python                         3.7.3      h8c8aaf0_0  pkgs/main
python                         3.7.3      h8c8aaf0_1  pkgs/main
python                         3.7.4      h5263a28_0  pkgs/main
python                         3.7.5      h8c8aaf0_0  pkgs/main
python                         3.8.0      hff0d562_0  pkgs/main
python                         3.8.0      hff0d562_1  pkgs/main
python                         3.8.0      hff0d562_2  pkgs/main

Then simple select the version conda install python=3.8.0 if this is the last version.

The folder containing your Anaconda installation contains a subfolder called conda-meta with json files for all installed packages, including one for Anaconda itself. Look for anaconda-<version>-<build>.json.

My file is called anaconda-5.0.1-py27hdb50712_1.json, and at the bottom is more info about the version:

"installed_by": "Anaconda2-5.0.1-Windows-x86_64.exe", 
"link": { "source": "C:\\ProgramData\\Anaconda2\\pkgs\\anaconda-5.0.1-py27hdb50712_1" }, 
"name": "anaconda", 
"platform": "win", 
"subdir": "win-64", 
"url": "https://repo.continuum.io/pkgs/main/win-64/anaconda-5.0.1-py27hdb50712_1.tar.bz2", 
"version": "5.0.1"

(Slightly edited for brevity.)

The output from conda -V is the conda version.