To read a Linux ext3 or ext4 external USB hard disk partition on Mac OS X, you will need to first install a third-party utility that allows Mac OS X to read and write to ext3 and ext4 partitions. One popular option is Paragon ExtFS for Mac, which is a commercial software tool that provides full read and write access to ext2, ext3, and ext4 file systems on Mac OS X.
To use Paragon ExtFS for Mac, you will need to purchase and install the software on your Mac. Once installed, you can connect your Linux external USB hard disk to your Mac and access the ext3 or ext4 partition just like any other hard drive on your Mac.
Alternatively, you can also use open source tools such as FUSE for OS X and Ext2Fsd to access ext3 and ext4 partitions on Mac OS X. These tools are free to use, but may not offer as many features as commercial software like Paragon ExtFS for Mac.
Regardless of which tool you use, you will need to make sure that the Linux external USB hard disk is properly formatted as either an ext3 or ext4 partition, and that it is connected to your Mac via a USB port. Once connected, you should be able to access the Linux partition just like any other hard drive on your Mac.