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From the parking area, an obvious trail (an old road) heads west into Macks Canyon. You can't drive down the road because it's blocked off. Follow the old road on foot about half a mile or so further into the canyon.
From time to time, small side canyons and drainages will branch off from the main canyon. You are looking for a small drainage branching off to the north (right) and marked by a cairn. If you find it, great - if not, no worries.
Whether you're successful or not in finding the correct drainage to leave Macks Canyon and head north, know that around 1/2 mile from the parking area you can safely work your way out of Macks Canyon and to the crest of the canyon above you. Fortunately, the north side of Macks Canyon tends to be slopey (if steep) rather than cliffy. Work your way to the crest above.
From the crest, Macks Peak may or may not be visible, depending on vantage point, but rest assured that it is just a short distance to the north.
Travel cross-country (there aren't any trails) to the north over undulating terrain until Macks Peak comes into view. Although Macks Peak's limestone walls seem somewhat intimidating and unpenetrable at first, it is very doable.
Work your way cross-country to the base of the cliffs near the southwest side of the peak. As you near the SW side, the occasional use trail and/or cairn should come into view. Follow them to and/or look for the only apparent way up the cliffs - a sloping narrow ledge heading west up the peak.
This ledge, covered in loose scree and only 18-inches or so wide in places, is about 50 feet long and exposed enough to hurt, but probably not kill, you. Carefully head up the ledge.
Once the top of the ledge is gained, follow sloping, scree-covered terrain upward toward obvious terrain allowing you to proceed.
Further description is not really necessary, as there's only one practical way to proceed and it's spelled out for you when you're there. Continue up class 2 and occasional easy 3 terrain to the right (north) around a bend and follow it up to the summit.
Typical warm weather hiking gear (boots, water, sunscreen, etc.) in the warm months.
Typical cold weather hiking/climbing gear in the cold months.