Cross Multiply
To cross multiply is to go from this:  \frac{8}{12} = \frac{2}{3} 

To this:  8 × 3 = 12 × 2 
How Does it Work?
Multiplying the top and bottom of a fraction by the same amount doesn't change its value.
Step 1: Multiply the top and bottom of the first fraction by the bottom number of the second fraction.
\frac{8 × 3}{12 × 3} = \frac{2}{3}
Step 2: Multiply the top and bottom of the second fraction by the bottom number of the first fraction had.
\frac{8 × 3}{12 × 3} = \frac{2 × 12}{3 × 12}
And Magic! The bottom of both fractions is now 12 × 3
Step 3: We can get rid of the 12 × 3 (as we are dividing both sides by the same amount) and the equation is still true:
8 × 3 = 12 × 2
Job Done!
In practice, though, it is easier to skip the steps and go straight to the "crossmultiplied" form.
Using Variables
OK, we have seen it with numbers, but now we can do it more generally using variables:
To cross multiply is to go from this: 
\frac{a}{b} = \frac{c}{d} 

To this:  ad = bc  
To remember think "cross" multiply:
Cross multiplication can help speed up a solution. Like in this example:
Example: Find "x" here:
\frac{x}{8} = \frac{2}{x}  
Let's cross multiply:  x^{2} = 8 × 2  
Calculate:  x^{2} = 16  
And solve:  x = 4 or −4 
Check: Does \frac{4}{8} = \frac{2}{4} and \frac{−4}{8} = \frac{2}{−4} ? Yes!
Terminology
I said "top" and "bottom" of the fractions ... but the correct words are numerator and denominator, OK? (I just wanted to keep it simple.)
Caution: Zero
Be careful, though!
We cannot use it when a denominator ("b" and "d" above) is zero, as dividing by zero is "illegal".