Here it says to provide a common name for the following carboxylic acid. So step 1 says we need to find the longest carbon chain and assign the name according to common name prefixes and endings. Now the parent chain should include the carboxylic acid group and have the most number of carbons. If I tie between longest chains, choose the chain with more substituents. If we take a look at this carboxylic acid, the longest chain would be here. And if we looked at this, it would be 1, 2, 3, 4 carbons. Four carbons for carboxylic acid, the prefix would be butyric, and it's a carboxylic acid, so it's butyric acid, or butanoic acid here would be the common name of the carboxylic acid itself. Now assign names to all substituents. Here we have a chlorine, which would be chloro. Here we have a methyl. Those are our 2 substituents.
Now, we're going to give the number using Greek symbols, which stands for the location for each substituent. Now when there is more than one identical substituent, we use prefixes like di for 2, tri for 3, and tetra for 4, and we name the substituents in alphabetical order. The prefix does not count towards the alphabetical order. Finally, when we put it all together, we are going to use commas between the Greek symbols, and we are going to use dashes to separate Greek symbols from letters. Letters are not separated by spaces.
When numbering the 4-carbon chain, remember this would be the alpha position, then beta, and then gamma. This would be the gamma position. If we look, chloro comes before methyl, so chloro is on the beta carbon, so this would be beta-chloro. Then, the methyl is on the alpha carbon, so this will be alpha-methyl. And methyl butyric acid is all one word. So this would be the name, beta-chloro-alpha-methylbutyric acid. Alright, this would be our final answer.