Suppose $X$ is a random variable with Pareto distribution. There pdf and cdf are:
$$f_X(x) = \begin{cases} {\alpha x_m^\alpha \over x^{\alpha +1}}, & \text{if $x\ge x_m$ } \\ 0, & \text{if $x\lt x_m$} \\ \end{cases}$$
$$F_X(x) = \begin{cases} 1-\left({x_m \over x}\right)^\alpha , & \text{if $x\ge x_m$ } \\ 0, & \text{if $x\lt x_m$} \\ \end{cases}$$
with $x_m\gt 0$ and $\alpha \gt 0$
Suppose $y=kX$, where $k$ is a non-negative constant. What are the pdf and cdf of $y$? Are there any restrictions on the value of $k$?
If $k=0$ then $Y$ is identically $0$. If $k\gt 0$, then for suitable $y$ we have $$F_Y(y)=\Pr(Y\le y)=\Pr(kX\le y)=\Pr(X\le y/k)=1-\left(\frac{kx_m}{y}\right)^{\alpha}.$$ The suitable $y$ are where $\frac{y}{k}\ge x_m$. Elsewhere we have $F_Y(y)=0$.
The density function $f_Y(y)$ can now be obtained by differentiating.
Alternately, look up the formula for $f_Y(y)$ given by the method of transformations, and integrate to find $F_Y(y)$.