The current React Native CLI requires node >= v8.3.0
Check your default node version
$ node -v
If your default node version is < v8.3.0 you need to update node or use nvm (recommended)
If you use nvm you need to set your default node version to v8.3.0 or later.
# Install the version that you would like
$ nvm install 8.3.0
# Set 8.3.0 (or another version) as default
$ nvm alias default 8.3.0
If you are using nvm you can - of course - always switch back to your old node version if needed for whatever project!
Hint: After you did set the default node version make sure to restart your terminal :)
When you are set you can install React Native CLI globally and it will use the default node version, in this example v8.3.0:
$ npm i -g react-native-cli
If you are on a Mac and want to build for iOS you probably need to sign the license agreement for Xcode. You can do this also via terminal:
$ sudo xcodebuild -license
$ react-native run-ios