Below is another method that works and may seem a bit simpler to some. It uses the SUBSTRING_INDEX MySQL function. A 1 returns everything before the first space, and a -1 returns everything after the last space.
This returns 'chara':
SELECT SUBSTRING_INDEX( field1, ' ', 1 )
This returns 'ters':
SELECT SUBSTRING_INDEX( field1, ' ', -1 )
Details
A positive value will look for your specified character from the start of the string, and a negative value will start from the end of the string. The value of the number indicates the quantity of your specified character to look for before returning the remaining piece of the string. If the character you are searching for does not exist, the entire field value will be returned.
In this case, a -2 would return everything to the right of the second to last space, which doesn't exist in this example, so the entire field value will be returned.