We are given an equation:
$$
\sqrt{12} - \sqrt{147} + y\sqrt{3} = 0
$$
To solve for $y$, we can isolate the $\sqrt{3}$ term on one side of the equation:
\begin{align*}
\sqrt{12} - \sqrt{147} + y\sqrt{3} &= 0 \\
y\sqrt{3} &= \sqrt{147} - \sqrt{12} \\
y &= \frac{\sqrt{147} - \sqrt{12}}{\sqrt{3}} \\
\end{align*}
To simplify the expression, we can rationalize the denominator by multiplying both the numerator and the denominator by $\sqrt{3}$:
\begin{align*}
y &= \frac{(\sqrt{147} - \sqrt{12})\sqrt{3}}{\sqrt{3}\sqrt{3}} \\
y &= \frac{\sqrt{441} - \sqrt{36}}{3} \\
y &= \frac{21 - 6}{3} \\
y &= \boxed{5}
\end{align*}
Therefore, $y=5$.