A life cycle assessment (LCA) compares the effect that products have on the environment. It follows a product through four stages: extracting and processing the raw materials, manufacturing and packaging, use and operation during its lifetime, and disposal at the end of its useful life. Transport and distribution are included at each stage.
Some of the impacts can be measured fairly easily. We can quantify the water used, the resources used, the energy sources used and the amount of some wastes made. The effect of a pollutant is different. Putting a number on how harmful a pollutant is means making a value judgement, so an LCA is not a purely objective process. Two people can score the same pollutant differently.
Quantified impacts can be added up across stages. If a bag needs 8 MJ of energy to make and 2 MJ to transport, the total for those stages is 8 + 2 = 10 MJ. A paper bag taking 12 MJ to make and 3 MJ to transport gives 12 + 3 = 15 MJ.
A selective or abbreviated LCA looks at only some of the stages or impacts. It can be misused to reach a conclusion that was decided before the work began, for example to back up a claim in an advertisement.
You may be asked to compare shopping bags made from plastic and paper. Plastic comes from crude oil, which is a limited resource. Paper bags need more water and energy to make, and are often thrown away after one use. Plastic bags can be used many times, but they last a long time as waste. Quantify an impact only where data is available, and compare the bags stage by stage.