Twice a number, increased by 6, is less than 48. what numbers satisfy this condition?

What you have to do here is write an inequality

"twice a number" = multiply it by 2
"increased by 6" = add 6
"less than 48" = < 48

so, with that:

2x + 6 < 48

then solve your inequality:

2x < 42

x < 21

so the numbers that satisfy this condition are numbers less than 21