Enhancers are important regulatory elements associated with eukaryotic genes. Here we present a random jump model on enhancer action at distance along the DNA. We show that to initiate the enhancing-action of an enhancer, a minimum jump size k=k(omega) which is directly proportional to the size of the genome, must be possessed by the RNA polymerase (RNAP) in the process of searching for the promoter sequences. When the jump size is near to or above k(omega), our model predicts that enhancers increase the level of expression of a gene mainly by increasing the probability of the gene to get transcribed rather than by increasing the transcriptional rate. Apart from this, our model also predicts that enhancer can increase the transcriptional probability only in the presence of the memory of the first time enhancer-RNAP contact. When the jump size associated with dynamics of RNAP on the DNA is close to or above certain critical values k=k(c) approximately 2N(2/3)where N is the length of the DNA under consideration, enhancers can regulate the transcription of a gene in a position and distance independent manner and at the jump size k=k(c) the enhancing action is a maximum. Since the jump size k is directly proportional to the degree of super-coiling or close-packed nature the DNA, our model suggests that to initiate the enhancer action a minimum degree of super-coiling of DNA is necessary that corresponds to the requirement of a minimum jump size k=k(omega) which agrees well with the experimental observations.