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\frac{2}{3}x+\frac{2}{3}\left(-4\right)=-\frac{7}{12}\left(x+6\right)
Use the distributive property to multiply \frac{2}{3} by x-4.
\frac{2}{3}x+\frac{2\left(-4\right)}{3}=-\frac{7}{12}\left(x+6\right)
Express \frac{2}{3}\left(-4\right) as a single fraction.
\frac{2}{3}x+\frac{-8}{3}=-\frac{7}{12}\left(x+6\right)
Multiply 2 and -4 to get -8.
\frac{2}{3}x-\frac{8}{3}=-\frac{7}{12}\left(x+6\right)
Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.
\frac{2}{3}x-\frac{8}{3}=-\frac{7}{12}x-\frac{7}{12}\times 6
Use the distributive property to multiply -\frac{7}{12} by x+6.
\frac{2}{3}x-\frac{8}{3}=-\frac{7}{12}x+\frac{-7\times 6}{12}
Express -\frac{7}{12}\times 6 as a single fraction.
\frac{2}{3}x-\frac{8}{3}=-\frac{7}{12}x+\frac{-42}{12}
Multiply -7 and 6 to get -42.
\frac{2}{3}x-\frac{8}{3}=-\frac{7}{12}x-\frac{7}{2}
Reduce the fraction \frac{-42}{12} to lowest terms by extracting and canceling out 6.
\frac{2}{3}x-\frac{8}{3}+\frac{7}{12}x=-\frac{7}{2}
Add \frac{7}{12}x to both sides.
\frac{5}{4}x-\frac{8}{3}=-\frac{7}{2}
Combine \frac{2}{3}x and \frac{7}{12}x to get \frac{5}{4}x.
\frac{5}{4}x=-\frac{7}{2}+\frac{8}{3}
Add \frac{8}{3} to both sides.
\frac{5}{4}x=-\frac{21}{6}+\frac{16}{6}
Least common multiple of 2 and 3 is 6. Convert -\frac{7}{2} and \frac{8}{3} to fractions with denominator 6.
\frac{5}{4}x=\frac{-21+16}{6}
Since -\frac{21}{6} and \frac{16}{6} have the same denominator, add them by adding their numerators.
\frac{5}{4}x=-\frac{5}{6}
Add -21 and 16 to get -5.
x=-\frac{5}{6}\times \frac{4}{5}
Multiply both sides by \frac{4}{5}, the reciprocal of \frac{5}{4}.
x=\frac{-5\times 4}{6\times 5}
Multiply -\frac{5}{6} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.
x=\frac{-20}{30}
Do the multiplications in the fraction \frac{-5\times 4}{6\times 5}.
x=-\frac{2}{3}
Reduce the fraction \frac{-20}{30} to lowest terms by extracting and canceling out 10.