Explicação passo-a-passo:

[tex] {64}^{x - 6} \: . \: {4}^{9x - 3} = {64}^{6x + 4} [/tex]

[tex]( { {4}^{3} )}^{x - 6} \: . \: {4}^{9x - 3} = ( { {4}^{3} )}^{6x + 4} [/tex]

[tex] {4}^{3x - 18} \: . \: {4}^{9x - 3} = {4}^{18x + 12} [/tex]

[tex] {4}^{(3x - 18 + 9x - 3)} = {4}^{18x + 12} [/tex]

[tex]3x - 18 + 9x - 3 = 18x + 12[/tex]

[tex]3x + 9x - 18x = 12 + 3 + 18[/tex]

[tex] - 6x = 33[/tex]

[tex]6x = - 33[/tex]

[tex]x = - \frac{33}{6} [/tex]

[tex]x = - \frac{11}{2} [/tex]