Jim can move 36 feet, or 35 feet (7 squares) if using the variant grid rules.
First, the rounding rule:
There’s one more general rule you need to know at the outset. Whenever you divide a number in the game, round down if you end up with a fraction, even if the fraction is one-half or greater.
So half-speed for Jim is 12.5 feet, rounded down, giving a speed of 12 feet. The rules for movement state:
On your turn, you can move a distance up to your speed.
Jim’s speed is 12, so he can move 12 feet with his usual move, and an additional 12 feet for each Dash, resulting in a total of 36 feet with his two available Dashes.
Using a grid is a variant rule.
Moving 5 feet at a time is not the standard rule for D&D, it is actually an optional rule, under the heading “VARIANT: PLAYING ON A GRID”. When playing on a grid, you use your movement in 5 foot blocks:
Rather than moving foot by foot, move square by square on the grid. This means you use your speed in 5-foot segments.
So with his usual move, having a speed of 12 translates to 10 feet of movement:
To enter a square, you must have at least 1 square of movement left
After using 10 feet (2 squares), Jim has 2 feet of movement left. You do not round a 12 feet speed down to 10 feet. You just have 2 feet of movement remaining after moving 10, which is not enough to enter a new square. Dashing twice adds 24 feet to his available movement, so he would have 26 feet of movement remaining, or 5 squares, which gives a total movement on the turn of 35 feet (7 squares.