4m - 2(3 + 2m) + m(2m + 4) = 0

Expand the brackets and factorize.

4m - (2 x 3 + 2 x 2m) + m x 2m + 4 x m = 0
4m - (6 + 4m) + 2m² + 4m = 0
4m - 6 - 4m + 2m² + 4m = 0
4m - 4m + 4m -6 + 2m² = 0
4m -6 + 2m² = 0
2m² + 4m - 6 = 0

Divide both sides by 2

m² + 2m - 3 = 0

Factorize the expression.

Two numbers when multiplied the resut is -3 and when added the result is 2. The two numbers are 3 and -1.

Express the 2m as 3m - m in order to be able to factorize.

m² + 2m - 3 = 0
m² + 3m - m - 3 = 0
m(m + 3)-1(m + 3) = 0
(m + 3)(m - 1) = 0
(m + 3) = 0 or (m - 1) = 0

m + 3 = 0
m = 0 - 3
m = -3

m - 1 = 0
m = 0 + 1
m = 1

m = -3 or 1

The L.C.M for the denominators (3x and x) is 3x, hence multiply each of the expressions by 3x to get rid of the fractions

4 = 21x - 3 x 3

4 = 21x - 9

13 = 21x

Divide both sides by 21

Cross multiply to get rid of the fractions

6 x 3(p+4) = 4 x (4p-1)

18(p+4) = 4(4p-1)

18xp+18x4 = 4x4p-4x1

18p+72 = 16p-4

Group the ps at the left hand side and the numbers right hand side

18p - 16p = -4 - 72

2p = -76

Divide both sides by 2

p = -38