SELECT * FROM `cars` WHERE 'model' = '$userchoice' AND 'sold = '0000-00-00'

looks fine, except for the backticks your using for column names.

In addition, you may wish to use MySQL Workbench to test your SQL. It is free and can be found MySQL :: Download MySQL Workbench.

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SELECT * FROM `cars` WHERE `model`='$userchoice' AND `sold` = '0000-00-00'

I corrected your syntax but other than that it is good. If you've set this up in PHP you want

$query = "SELECT * FROM `cars` WHERE `model`='{$userchoice}' AND `sold` = '0000-00-00'";

Thanks this is great post.It give me some good tips about PHP.I want to learn more about PHP.

While that works, that is not exactly best practices, as well as works for that exact case. It might be better off to convert the date to unix timestamp, and work with it that way. The syntax for converting a string to unix timestamp is...
UNIX_TIMESTAMP

and you can read a brief tutorial on it <a href="http://stackoverflow.com/questions/3413559/mysql-convert-mm-dd-yy-to-unix-timestamp">here</a>

Also, another practice is to grab all of the dates, and then use strtotime in php and manipulate the dates that way.

so in your instance, you would have done something like...

I'm using SELECT * FROM `cars` WHERE `model`= "$userchoice" AND FROM_UNIXTIME(`sold`) > 0