The expression described is translated into the following formula:
[tex] \frac{x+6}{2x} = \frac{3}{4} [/tex]
Note that this implies that [tex] x \neq 0 [/tex]
Cross-multiply denominators to get rid of the fractions:
[tex] 4(x+6) = 3(2x) [/tex]
Expand both sides:
[tex] 4x+24 = 6x [/tex]
Subtract 4x from both sides:
[tex] 24 = 6x - 4x = 2x [/tex]
Divide both sides by 2:
[tex] 12 = x [/tex]
Check:
[tex] \frac{12+6}{24} = \frac{18}{24} = \frac{3}{4} [/tex]
Which is true because
[tex] 18 \cdot 4= 24\cdot 3 [/tex]
since both sides evaluate to 72
