With 19,20,21,23 i don't understand geometry at all

19.  What you know is that HK+KJ = HJ.  If HJ = 25, the sum of the two equations will equal this length.  

x-5+5x-12=25  First, combine your like terms.  You will end up with 6x-17=25.  Add the opposite of -17 to both sides.  6x = 42  Divide both sides by 6.  x = 7.  Substitute x=7 for your original expression of x-5, 7-5=2

20.  (5x-6)/2 = x+6  Multiply each side by 2.  5x-6 = 2x +12  Add 6 to each side 5x = 2x + 18 then subtract 2x from both sides as well.  3x = 18 Finally divide each side by 3.  x=6   To find the length of the remaining segment, substitute this value into (5x-6)/2.  This results in each side equaling a distance of 12.

21.  On the number line, the distance of FG is 16 units.  If the distance of FP is 1/4 of FG, you would simply divide 16 by 4.  The distance of FP is 4 and P lies at 8 on your number line.

23. The distance of SP is x+4 and ST=4x.  Since P is the midpoint, you only have one half of the line as x+4, if you were to double it, you would find that 2x+8 = 4x.  Balance and solve for x, subtract 2x from both sides. 8=2x  Divide each side by 4, 8/4 = 4x/4 resulting in x=2.  If ST equals 4x, substitute and solve, 4(2) = 8