First of all, lets give names to the quantities we're dealing with. Let be X = #Boys and Y = #Girls.
The first piece of information we're given is that the total number of students is 26, thus the number of boys and the number of girls should add up to 26, this gives us the first equation:
X + Y = 26
The second piece of information we're given is that the number of girls is 4 fewer than twice the number of boys. That means that the number of girls equals twice the number of boys minus 4. Putted onto an equation gives us:
Y = 2X - 4
Now all we have to do is to solve this system of two by two equations. The easiest way to do this is to replace the Y value from the second equation onto the first one. Thus, yielding:
X + (2X - 4) = 26
3X - 4 =26
3X = 30
X = 10
Now we replace X = 10 onto the second equation, that gives us:
Y = 2*(10)-4
Y = 20 - 4
Y = 16
That means that 10 boys and 16 girls attended the event.