Two dogs barking independently uniform distribution

Question

Two dogs are in front of your house. The first barking of the two dogs are independent of each other, and may occur at any time uniformly within 4 seconds after opening the door, and then each dog barks at an interval of 4 seconds. If the two dogs both notice you opening the door at the same time, what is the probability that the difference between their first barking moments is no more than 2 seconds?

$f(x) = \int probability(>) , 0<x<4 $

i know that the uniform distribution is bounded by 0 and 4,

but i do not know what to do to go further from this question

Honestly very lost and do not know where to start

Answer 1

Here is a hint, which may help

Answer 2

They are requesting you to calculate the following probability

$$\mathbb{P}[|X-Y|<2]$$

doing a drawing of the situation you get that the "good" region is the purple one

Of course it is easier to calculate the complement probability, thus

$$\mathbb{P}[|X-Y|<2]=1-\frac{4}{16}=\frac{3}{4}$$