4/(2x)=5/(x+6) Solve the equation by cross multiplying. Check for extraneous solutions.

Cross multiplying is something students tend to struggle with.  I always think of cross multiplying like drawing butterfly wings on my paper.  You can draw one wing from the numerator on one side of the equation to the denominator on the other side.  Draw the second wing capturing the remaining numerator and denominator.  These wings show you what to multiply. Write out your equation, using your wings for help, and be sure to separate the two sides of the equation with an equal sign.
4(x+6) = 5(2x)
Distribute to simplify, being sure to distribute the 4 on the left hand side of the equation to both terms inside the parentheses.
4x+24=10x
From here you have two options on how to proceed.  The first option is very appropriate for a more cut and dry problem.  Combine the like terms by using algebra.  The 4x and 10x are like terms so we want to get them on one side of the equation.  The goal here is to isolate the x, or solve for x.  Since my goal is to isolate the x, I am going to move the 4x by subtracting it from both sides of the equation.  Doing so leaves me with 
24=6x
x=4
Check for extraneous solutions by plugging your answer of 4 back into the original equation for x.  If both sides of the equation match after simplifying, your answer is correct.  If the values do not match, the answer is extraneous or false.

4/8=5/10 
Since both sides of the equation equal 1/2, the solution is not extraneous.
 
Side Note:  The other option for solving the equation would be to move all terms to one side of the equation so the equation is set equal to 0.  To do this, I would suggest subtracting 10x from both sides.  This would leave
-6x + 24 = 0
From here, you could factor out a greatest common factor of -6 from the left hand side of the equation.  This would leave -6 ( x – 4) = 0. 
Set the factor of ( x – 4 ) equal to 0 and solve for x.   Note that the -6 in front of the parentheses has no effect on the solution because it does not contain a variable like x. 
Solving for x again yields x = 4. 
Option 2 is very useful for more complex problems containing quadratics (x2 terms). 

4/(2x)=5/(x+6)
Cross multiply,
4(x+6)=5(2x)
4x+4*6=10x
4x+24=10x
4x-10x=-24
-6x=-24
x=(-24)/(-6)
x=4
Check the solution:
4/(2*4)=5/(4+6)
1/2=5/10
1/2=1/2
It's true.
So, the solution is x=4