logarithms

7^(6x)-2=10
7^(6x)-2+2=10+2
7^(6x)=12
logarithm on both sides:

ln( 7^(6x) ) = ln( 12 )
6x * ln( 7 ) = ln( 12 )
x = ln(12)/(6*ln(7))
x = 0.2128