This is simple as long as you remember FOIL:
First
Outside
Inside
Last
So, for example, let's multiply out (2x+1)(4x-3)
Multiply the first number from each bracket together: 2x times 4x = 8x2
Then the outside from each bracket: 2x times -3 = -6x
Then inside: 1 times 4x = 4x
And outside: 1 times -3 = -3
Then add all these together: 8x2 -6x +4x-3
Final answer: 8x2 -2x -3