Solve for a 2a-b=8b-4a

$2 a - b = 8 b - 4 a$

Move all terms containing $a$ to the left side of the equation.

Add $4 a$ to both sides of the equation.

$2 a - b + 4 a = 8 b$

Add $2 a$ and $4 a$ .

$6 a - b = 8 b$

Move all terms not containing $a$ to the right side of the equation.

Add $b$ to both sides of the equation.

$6 a = 8 b + b$

Add $8 b$ and $b$ .

$6 a = 9 b$

Divide each term in $6 a = 9 b$ by $6$ and simplify.

Divide each term in $6 a = 9 b$ by $6$ .

$\frac{6 a}{6} = \frac{9 b}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 a}{6} = \frac{9 b}{6}$

Divide $a$ by $1$ .

$a = \frac{9 b}{6}$

Simplify the right side.

Cancel the common factor of $9$ and $6$ .

Factor $3$ out of $9 b$ .

$a = \frac{3 (3 b)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$a = \frac{3 (3 b)}{3 (2)}$

Cancel the common factor.

$a = \frac{3 (3 b)}{3 \cdot 2}$

Rewrite the expression.

$a = \frac{3 b}{2}$