I am having a hard time getting started on this.

n*3^{n}<= 4^{n}-2

where n>6

I have done the start step setting n = 7 and affirming that it is true.

and I assume

k*3^{k}<= 4^{k}-2

but I cannot grasp how I should prove

(k+1)*3^{(k+1)}<= 4^{(k+1)}-2

Thank you