Vehicle surround project, Multiple sensors and output to display.

I have a project idea and I am not sure if I should use the arduino or raspberry pi. My project is to use 6 HC-SR04 ultrasonic sensors to have them sense if an object is to the left, right, front, or rear of an vehicle. The output will then be sent to a monitor that will alert the user if an object is approaching from a particular direction. Can this be done with the arduino?

I would just need to connect 6 sensors to the device, compute the distances, then output to a display and the direction that the object is approaching.

I would say that, yes, you can do this with an Arduino.
Just don't try to update too frequently - that's a common problem.
An aggregate update rate of around 20Hz is sensible, unless you deliberately knobble the sensitivity of the sensors.

You need two pins per sensor so so you could easily put four on a basic Arduino (UNO, Leonardo, Micro, Nano, or Mini). The NewPing library has an example sketch showing how to connect 15 ultrasonic distance sensors to an Arduino MEGA 2560. You can adapt that to a smaller number of sensors.