this will bit you in the backside.
as a general rule use ' to delimit strings
eg
myvariable = 'this is an example'
although with Access you can use " as well
theoretically you can use "" to use the " symbol inside text. but it can get messy very quickly, especially if you are intending pumping data into another database. I'd strongly recommend you use ft in in place of ' " eg 6ft4in, or leap forward into the 19th century and use the metric system for measurements eg 1.88m

. the problem is not storing the data in Access, or in MySQL its pushing it from Access to MySQL. you can get round it by telling Access to export the file using another symbol to delimit strings and tell MySQL to use the same symbol to import strings. its a mess