Find the measures of two supplementary angles if one angle is 6 degrees less than twice the other

180= x+ 2x-6

186=3x

62=x

so one angle is 62 degrees

the other is:

2(62) - 6
= 118 degrees

Supplementary angles equal 180 degrees when put together, so if one angle was 87 degrees and the other 93 degrees, they would have a difference of 6 degrees and would total 180 degrees, as is required for supplementary angles.

translate the phrases in the question into expressions in an equation:
two supplementary angles--angle_1 + angle_2 = definition_of_supplementary_angles
one angle is 6 degrees less than twice the other--angle_1 is the other angle_2 = 2*angle_1 - 6

substitute and solve