In order to win the Germans must capture and hold for one turn one of the hexes containing a manpower symbol. These can be seen by making units invisible. They are all on the roads leading into Budapest and each is 5 km from the city. The premise is that the capture of any one of these is close enough to the city to enable a breakout by the garrison.

The Soviets win by capturing the Axis Supply point hex (and holding it for one turn) in Buda.

If the game reaches turn 70 (Feb. 5) without either side winning in the ways described above, then the game is a draw.

For the first 6 turns Axis supply is 40. This models the inevitable pre-offensive stockpiling that must have went on.
Beginning on Turn 7 these stockpiles are assumed to be exhausted and Axis supply drops to 25.

Soviet supply is 33 throughout the game.

Turn 1 = 120. Turn 3 = 110. Turn 5 and after = 100.

Turn 1 = 80. Turn 3 = 90. Turn 5 and after = 100.

SS units receive units at the HIGH rate.

Slovak units are set at LOW or VERY LOW.

Everybody else is NORMAL except units inside the pocket. Hungarian Honved units can tap the local populace and so receive a VERY LOW rating. The two SS cavalry divisions were composed of Germans of Hungarian descent and so also get a VERY LOW rate. Other Hungarian units in the pocket are either fanatics or militia, and so are set to NONE. Note that these comments apply only to units containing no heavy equipment such as tanks and artillery. Units in the pocket containing heavy equipment are set to NONE.

Guards units and regular army Mechanized and Tank corps are set at HIGH. Romanian units are set at VERY LOW. Everything else is NORMAL.

The Germans get a couple of Panzer Divisions in the North at around turn 12. They will need them to stem the Russian counterattack there and that is how they were used historically.

There is a significant Luftwaffe reinforcement at around turn 36.

Between game turns 20 and 50 the Russians receive a Tank Corps and two Mechanized Corps.

One of the Panzer corps received at move 12 is withdrawn later in the game.

Your road is hard but not hopeless. Your first thought will be to drive with 4 SS PzK towards the nearest manpower point in front of the city. This is what the Germans did. The Russians, however, are (and were) deployed to counter this. But who knows ? With a little luck ( a key soviet unit reorganizes at an opportune time etc. ) you might make it. Another option is to delay moving the Panzer units near the Lake with the hope of drawing all the Soviet mobile reserves into the fight east of Buda with 4 SS PzK and then launching a secondary strike from the south. This idea has potential, but a good Soviet player will be able to stop it.
The PO does take it into account, but Elmer is what he is. You could also try something else the Germans actually did, which is pull 4 SS PzK out of the fight in the north at an opportune moment and redeploy it in the south to support a delayed thrust there. This is the option must likely to cause Elmer trouble; it is, however, also the most difficult to undertake.
Redeploying a heavy engaged Panzer Korps is not for the faint of heart. Lastly, by trying all these things you may keep the Russians so busy moving their mobile reserves around that they only have Rifle divisions to assault Budapest with and so fail, thus ensuring a drawn result; and make sure you have a plan to meet the inevitable Soviet counter-attack up north.

Read the above and plan accordingly.