Use the following limit definition to determine the slope of the line tangent to the graph of $f$ at $P$, where $f\left(x\right)=\frac{4}{3x-2}$ and $P(0,-2)$:
$m_{\text{tan}}=\underset{h\to 0}{\lim }\frac{f(a+h)-f\left(a\right)}{h}$