By definition, a function $f(x)$ is continuous at $a$ if and only if:
- $f(x)$ is defined at $x=a$;
- $\lim\limits_{x\to a}f(x)$ exists; and
- $\lim\limits_{x\to a}f(x) = f(a)$.
So for your $f(x)$ to be continuous at $0$ you need it to be defined at $0$ (which it is), and you need $L = f(0) = \lim\limits_{x\to 0}f(x) = \lim\limits_{x\to 0}\frac{\sin(0.19x)}{x}$ to be true.
Since you are free to decide what you want $L$ to be, what you need to do is figure out how much that limit is.
HINT: you've probably recently seen the fact that $\lim\limits_{u\to 0}\frac{\sin u}{u} = 1$. Try to use that.