Let [tex]l,w[/tex] be the length and width of the rectangle, respectively.
On the one hand, we know that [tex]l = 4w-6[/tex]
On the other hand, we know that
[tex]2(l+w)=176[/tex]
If we substitute the expression for l, we have
[tex]2(4w-6+w)=176 \iff 5w-6 = 88 \iff 5w = 94 \iff w = \dfrac{94}{5}[/tex]
And we can deduce
[tex]l = 4\cdot\dfrac{94}{5}-6 = \dfrac{346}{5}[/tex]
