Employees in 2012 paid 4.2% of their gross wages towards social security (fica tax), while employers paid another 6.2%. how much will someone earning $28,000 a year pay towards social security out of their wages

If you have worded the question verbatim from the problem, then you only need to worry about the 4.2% paid by the employee out of his/her gross.

(If you altered the wording a bit, then the 6.2% from the employer may factor in somehow. But the way the problem is worded above, it does not.)

If I make $28,000 and paid 4.2% out of my wages myself, then that would be

28,000 x .042 = $1176 toward SS that I paid myself from my gross wages.