Imagine a two-dimensional space defined as a 6x6 grid. You are positioned at the bottom-left corner and your goal is to reach the top-right corner of this grid. The only allowed movements are: you can go right (to the adjacent cell in the same row) or you can go up (to the adjacent cell in the same column). Movements to the left or downwards are not allowed. The question is, how many distinct paths can you follow from the bottom-left corner to the top-right corner under these constraints?