Step 1:

$X\sim P(4)$

$\therefore P(X=x)=\large\frac{e^{\Large -4}4^{\Large x}}{x!}$$\qquad x=0,1,2....$

Step 2:

$P(X\leq 3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)$

$\qquad\qquad=e^{\Large -4}\big[\large\frac{4^0}{0!}+\frac{4^1}{1!}+\frac{4^2}{2!}+\frac{4^3}{3!}\big]$

$\qquad\qquad=0.0183\big[\large\frac{(1+4+8)3+32)}{3}\big]$

$\qquad\qquad=0.0061[71]$

$\qquad\qquad=0.4331$