Jessica:
The mathematically correct answer is 14. That's because each operator (+, -, etc.) has a place in the hierarchy and those in higher levels must be processed before those in lower levels. Since x has a higher hierarchy level than +, multiplication comes first (3x4=12), then followed by addition (2+12=14).
Algebraic calculators come in two very distinct flavors. The first, or older, pays no attention to the operator hierarchy. Operations are simply carried out in the order in which they are entered -- from left to right, no exceptions -- and so often yield incorrect answers. The second, or newer, does pay attention to the operator hierarchy. Operations are carried out in the mathematically correct order, yielding correct answers. RPN calculators have never had this problem, since it's the user who supplies the order of the operations.
When I say "older" and "newer" I don't mean the age of the calculator, but of its operating system. Even today you can buy simple 4-function calculators that use the older version, without hierarchy. Usually -- but not always -- those algebraic calculators that have parenthesis keys are the ones that give the correct answers. WHEN IN DOUBT, USE PARENTHESES.
I don't agree with the assessment that the Calculator in Windows is OK because it follows the most common interpretation, even though it's the wrong one. A calculator is EXPECTED to provide the right answer; if it doesn't, its only place is the waste basket.
By the way, other games can be played with algebraic calculators of the old style. If you alter the order of the operands in commutative operations (+ and x), sometimes you get different answers if the expression includes other operations. For example:
2 + 3 x 4 = 20
2 + 4 x 3 = 18
Watch out for expressions that include powers of powers (such as 4^3^2). The "raising to power" operation (usually y^x in most calculators) is THE exception to the rules of order of operation -- even in mathematics. 4^3^2 must be calculated as 4 raised to the power 3^2 -- that is, 4 raised to the 9th. In other words, if you find a string of powers, they must be executed from right to left (!).
In these cases, you may have the same number several times (such as 3^3^3) and obtain two different answers depending on which ^ operator you execute first:
(3^3)^3 = 27^3 = 19,683
3^(3^3) = 3^27 = 7.63 E 12
The second one is the mathematically correct answer, if the parentheses were removed.
A few calculators (such as TI's SR-51A) have no parenthesis keys, yet do follow the hierarchy, but only up to a certain point. In my opinion, that's the worst kind of calculator there is. Some HP business calculators are the opposite: they have the parenthesis keys but do not pay attention to operator hierarchy.
Again, when in doubt, use parentheses.
Happy calculating.
-EM