I have a result from which I want to get significant genes (pvalue-threshold=0.1, log2FoldChange threshold 1.5), and divide them into up-regulated and down-regulated.

From the vignette, I found the following on down-regulation and up-regulation:

subset the results table to these genes and then sort it by the log2 fold change estimate to get the significant genes with the strongest down-regulation:

resSig <- subset(res, padj < 0.1)     
head(resSig[order(resSig$log2FoldChange), ])

…and with the strongest up-regulation:

head(resSig[ order(resSig$log2FoldChange, decreasing = TRUE), ])

So, based on this, I wanted to ask whether I can achieve correctly what I have mentioned above by the following or not:

resSig <- subset(res, padj < 0.1)
up_regulated <- subset(resSig, log2FoldChange > 1.5)
down_regulated <- subset(resSig, log2FoldChange < 1.5)

Kindly guide if this is a wrong approach.

This is fine, however we recommend inserting LFC thresholding into the specification of the null hypothesis:

res <- results(dds, lfcThreshold=1)
resSig <- subset(res, padj < 0.1)
upReg <- subset(resSig, log2FoldChange > 0)
downReg <- subset(resSig, log2FoldChange < 0)

Note that LFC > 1 in the null hypothesis stage will give you similar results as simple thresholding of 1.5.