Well duh. You draw the back side in a bitmap editor. Then in-game instead of the face of the card you draw the back side.

Check the values of mouse_x, mouse_y and mouse_b&1 and when they indicate a card has been clicked, play the flip animation. A simple way to do this is to progressively stretch the back side to a smaller size in one dimension and then when it reaches 0, progressively draw the face stretched to a bigger size until it reaches full size.

install_mouse()
RTFM, the rest of the mouse routines section as well. You can have Allegro or the underlying system draw the mouse cursor for you, or you can draw it yourself with draw_sprite().

Yes. RTFM, the sections about timers and text output.

Welcome, jetzfan.

Sounds like you need to keep track of the card states somewhere; like have a int flipped_flag with possible values 0=facedown and 1=faceup.

See Miran's post; installmouse(); There should be a program in the examples that uses the mouse, you can check that to see how it's done.

Again, see the examples to see an example of using timers.

C or C++?

Hope that gives you an idea, I've commented out the code you are supposed to implement, but it should give you a framework to start with.

There is a ton of ways to do it but here is my example:

Untested but I hope it gives you an idea, you go through each type of card and assign it to a random index of your array if it's not already taken. You have to do it twice because there are two of each card. This is just one way of doing it out of many.

Nothing in code happens magically, this is the way I know and it should work. If you want simpler than I suggest trying something else, get a good C book and read up on stuff before jumping into a graphical game environment. I'm not sure what you mean by simpler.

yep...here it is:

#include <allegro.h>

void init();
void deinit();

int main() {
init();

//before the game page there are two other pages that I have no problem with

//game page
install_mouse();
show_mouse(screen);
int c;

BITMAP *img3, *cursor, *cursor2, *cursor3, *cursor4, *cursor5, *cursor6;

img3 = load_bmp("c:\\familyguylogo.bmp",NULL);
cursor = load_bmp("c:\\PETER.bmp",NULL);
cursor2 = load_bmp("c:\\LOIS.bmp",NULL);
//etc.....

blit(img3, screen, 0,0,0,0,640,480);
stretch_blit(img3, screen, 0,0, img3->w, img3->h, 0,0, SCREEN_W, SCREEN_H);

draw_sprite(screen, cursor, 50, 75);
draw_sprite(screen, cursor2, 50, 200);
draw_sprite(screen, cursor3, 195, 75);
draw_sprite(screen, cursor4, 195, 200);
draw_sprite(screen, cursor5, 337, 75);
draw_sprite(screen, cursor6, 337, 200);
draw_sprite(screen, cursor, 480, 75);
draw_sprite(screen, cursor3, 480, 200);
draw_sprite(screen, cursor3, 50, 325);
draw_sprite(screen, cursor4, 195, 325);
draw_sprite(screen, cursor5, 337, 325);
draw_sprite(screen, cursor6, 480, 325);

for(c=0;c<2000000000;c++);
system("cls")

yeah i've heard of arrays. what are mockup tags?

OK, let me guess - before C you have written your programs in BASIC?

My advice is to learn the language you are dealing with. You don't know about the basic features of C, so you are obviously stuck with no knowledge.
Just one example:
Instead of calling your variables cursor,cursor2,cursor3,cursor4,... you can do the following:

BITMAP *cursor[6];
cursor[0] = load_bmp("...bmp",NULL);
cursor[1] = load_bmp("...bmp",NULL);
...

That way you can say

for (c=0;c<6;c++)
{
  draw_sprite(screen,cursor[c],c*100,10);
}

or something like that.

And instead of

for(c=0;c<2000000000;c++);

you can say (in Allegro)

rest(2000);

which will pause your game for exactly 2 seconds (2000 1/1000s of a second).

Of course these are just basic concepts and they won't give you a memory game. You have a lot to learn. First try to cope with C, and then with Allegro.
[append]
On a second thought you could make a memory game by making use of the little programming knowledge you have, but I'm afraid you wouldn't learn anything. Trust me, I've seen huge games from newbies like you, some guys even managed to do (text-based) RPGs without using loops, because they just didn't know them.
Nevertheless I encourage you to learn at least the basics of C (;D pun) before continuing.

Yes, nothing after system("cls") though? I don't know how you managed to get that to compile.

Read Simons post, he said it best. I'm not sure I can help you much more.

You have to use both..... Make the game like you would with an array, then use allegro to give it a graphical interface. This is were the creativety comes into programming; to explain better would be to program it for you?