Yes you can. You don't have to download both Anaconda.
You can have both versions installed at the same time.
can I install multiple versions of Python on my machine? can I install multiple versions of Anaconda? You can but because of the answer above you don't need to and shouldn't. Instead of multiple Anaconda versions, just create multiple environments with the versions of packages you need.
There is no need to install Anaconda again. Conda, the package manager for Anaconda, fully supports separated environments. The easiest way to create an environment for Python 2.7 is to do
conda create -n python2 python=2.7 anaconda
This will create an environment named python2 that contains the Python 2.7 version of Anaconda. You can activate this environment with
source activate python2
This will put that environment (typically ~/anaconda/envs/python2) in front in your PATH, so that when you type python at the terminal it will load the Python from that environment.
If you don't want all of Anaconda, you can replace anaconda in the command above with whatever packages you want. You can use conda to install packages in that environment later, either by using the -n python2 flag to conda, or by activating the environment.
Edit!: Please be sure that you should have both Python installed on your computer.
Maybe my answer is late for you but I can help someone who has the same problem!
You don't have to download both Anaconda.
If you are using Spyder and Jupyter in Anaconda environmen and,
If you have already Anaconda 2 type in Terminal:
python3 -m pip install ipykernel
python3 -m ipykernel install --user
If you have already Anaconda 3 then type in terminal:
python2 -m pip install ipykernel
python2 -m ipykernel install --user
Then before use Spyder you can choose Python environment like below!
Sometimes only you can see root and your new Python environment, so root is your first anaconda environment!

Also this is Jupyter. You can choose python version like this!

I hope it will help.
This may be helpful if you have more than one python versions installed and dont know how to tell your ide's to use a specific version.
anaconda. Latest version can be found here
anaconda-navigator in terminalcreate and then choose your python version in that. install in that. Hope it helps!!
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