Is the monthly order of six hexagrams calculated by solar terms?

Yes, the map of returning to Tibet in December defines the December branch with twelve news hexagrams, that is, the twelve solar terms divide December. You can check the China perpetual calendar of Nanjing Observatory to find the solar terms of that year. From beginning of spring to the first month, the first month is silver moon; From the first month to the Qingming Festival, it is Uzuki in February; From Qingming to long summer, it is March; From the long summer to the middle, it is Mitsuki in April; From the boundless to the small tree, it is the afternoon of May; It is the last month of June to arrive in beginning of autumn in the summer. From beginning of autumn to the Millennium, it is a single August; From the cold dew to beginning of winter, it is the full moon in September; And from beginning of winter to heavy snow, it is October.