Ratio Test

a(n + 1) = (-10)^(n + 1)/{[ 2(n + 1) + 6] [ 8^(n + 1 + 3)]}
= (- 10)^(n + 1)/[ (2n + 8) 8^(n + 4)]
So a(n + 1)/an
= (-10)(2n + 6) 8^(n + 3) / (2n + 8) 8^(n + 4)
= (-10)[2n(1+ 3/n)/2n(1 + 4/n)] 8^(-1)
= (-10)(1 + 3/n) 8^(-1)/(1 + 4/n)
When n tends to infinity, the absolute value of the ratio tends to |(-10)/8|
= 5/4 > 1.
Therefore, the series does not converge.